Really long post but I had the time to do a bunch of voice to text over coffee this morning so I hope some of this at least might help you or someone else reading it in the future.
Something occurred to me and I know this has been a ongoing issue for over a year now basically. When you're running the boat on a garden hose, you must kill the water before the motor dies. Motor always has to be running before the water is turned on and after the water is turned off or the water can back up in the system entering your oil next. With all of the experience you have on this so far I'm assuming you already know this but wanted to add that in just in case.
Regarding the unit not having any oil in it during that other previous comment.... just wanted to make sure that you realize this is known as a dry sump motor meaning that before you run the motor at all, after a long period of sitting, you will have zero oil to maybe one quarter of an inch maximum on the bottom of the dipstick when you first check the level on a completely cold motor. If the boat is completely and I mean completely level and the oil is absolutely perfectly filled to manufacturers specification this will be the case. Oil is checked on these motors after running for at least 5 minutes then kill the engine and test immediately to determine perfect proper oil level. I have a feeling that you are also already aware of that.
The reason your oil was overfilled on your most recent experience with that, assuming that you were already aware of the dry sump principle on this, is because you're fuel injector was running continuously and therefore the fuel was washing out the piston rings allowing the fuel to drain down past the Rings into the oil pan diluting the oil making it appear to be filled up all the way to the cap with oil. I've had this happen on nfxho Waverunner before myself with the injector being stuck. Most people tend to think the ECM is the reason why these injectors get stuck and they send them out to California to have a company out there rebuild the ECM for $400 including new fuel injector relays. On my particular WaveRunner that had the stuck open fuel injector it was actually because the fuel injector itself was faulty. Tested that theory by swapping that same injector onto a different cylinder and it still continuously sprayed even though it would now be firing from a different injector relay inside the ECM that was previously functioning perfectly. Double checked that by swapping the ECM and the exact same thing happened. Replaced the injector and everything works fine.
I believe you said you already replaced all of the injectors so that was a good move. If you have not heard of or have not considered the ECM being a problem that is worthy of consideration if you continue to get a buildup of thinned out oil in your reservoir.
The SBT Motors are garbage. I don't mean that anecdotally. I've been building these motors a long time and I have pulled apart plenty of fxho SBT builds as well as vx110 builds. Every time I pull it apart I find that torque specs removing the bolts are inconsistent, head gaskets are compromised, or rods are broken. When they rebuild their Motors they do use Chinese manufactured components. I don't necessarily have 100% problem with Chinese components however I also believe that the vx110 and the fxho rods that are used are the exact same rod for both motors. If you look at the parts list on Yamaha parts supply websites they are different rods. The VX turns at approximately 8,000 RPMs and the FX turns at 10,000 rpms. These rods are different because the FX needs beefier more robust rods to handle those forces. The compression is the same and the Piston size is the same. The Pistons on both of those skis are actually different when they come from japan. Again, a little more robust on the FX but not on the sbt. I have also found bearing clearance issues in the SBT Motors when reassembling them and doing a proper squish test using plasti gauge methods. Then I put the bearings in a temperature controlled environment along with the OEM matching size and tested the thicknesses with micrometers and came up with different thicknesses on the SBT bearings versus oem.
I have also used their 100% Chinese clone fxho Motors and just received one back that is less than 2 years old after a 100% catastrophic motor destruction from a valve dropping. 1 of the Pistons was 100% completely gone, missing in action, destroyed leaving no signs of itself at all inside the cylinder when I opened it up. It had been completely destroyed into particles and had dropped down into the oil pan past the crank. Shockingly, the rod and the Pistons wrist pin we're still in place intact and the crank is untouched as far as scarring or damage. The head is destroyed on that cylinder, two of the valves are missing on that cylinder, both of the buckets and shims are missing inside the head and completely got destroyed and eaten by the machine inside the head itself. I've never seen this before in plenty of motors and lots of time on forums over the years. I fully believe this motor was destroyed from inside the head when something came apart up there. I feel fairly confident it was due to the clearance issues between the cams and the buckets over the shims but this is subject to best guessing when it comes down to it.
I say all of this simply to say good call getting a donor ski instead of another sbt. I'm done with them on these four stroke Motors. They can be a good temporary solution but longevity is never going to be there in my opinion. The Chinese ones are flat garbage at the price they charge IMO and what good is a warranty on something that the average guy can't DIY install having to pay for removal and replacement cost every time just due to poor workmanship and poor quality parts?
You might want to suspect your ECM causing some problems and keep an eye on that. Check your oil level and inside that air box housing around your intake regularly during water runs to make sure it's not sucking in oil for a while.
As far as your water leak goes, if you are certain that your actual jet pump plugs are not leaking then it sounds like you have an underpower leak from somewhere else. Common leak points on these are going to be through the forward portion of your intermediate shaft bearing housing. Those wear out and will let water flow in around that black front rubber section about the size of a softball in diameter. Also, considering how many times the motor has been in and out of there I would more so suspect a poorly secured hose clamp around one of the many water box fittings behind the exhaust pipe coming out of the port side of one of those motors (suspect starboard motor of course). After that I would suspect a cracked rubber water supply hose. I would not necessarily suspect one of the draining hoses but the water supply itself.
Another common leak can be from the bilge pump itself. If you follow the bilge pump rubber hose it will come up to a little 90° typically black plastic fitting. Inside of that fitting there is a rubber duck bill shaped one way check valve. The diameter of the check valve is about the size of a nickel. It's easy to separate this housing to check and pull that duckbill valve out. If the lips on the duck bill are perfectly flat with no debris in them then this is probably not your problem. If the lips are pursed at all then I believe you have a water leak from the boat actually taking a backwards siphon while at rest allowing the water to dump into your bilge. If you're getting water from sitting in the water floating for a while without running the boat this would be my suspicion. If you're getting water pouring in while underway it is not my suspicion.
Other places I have seen Motors take water on are if the bilge itself gets filled with water while the motor is running and if there are any air leaks in the motor on the bottom end where the water pools up, the motor can suck water in and mix it with your oil via Venturi effect. This would be common if you have a loose oil pan or any other bad o-ring style connection maybe between the oil reservoir itself and the rear end of the motor. If this was the case you would also be seeing oil show up in your bilge after the boat has set up for a while slowly leaking out of that same hole. If you don't have fresh oil sitting under the motor after long storage this is not my suspicion.
Another place we have seen water enter the motor especially on sbt replacements, is on that stainless steel water pipe coming out of the top of the head. Inside of there there is a single o-ring seal and if it has any chafing or irregularities allows water to Bubble Up and flow out of the black rubber trim cap around it directly into the boat. The cylinder head cover itself has another gasket on the outside diameter of that area that keeps the same water from being able to enter the cylinder head itself. If that is not installed correctly by SBT or someone else it can cause a water leak directly into the motor from that area. Simply pulling the rubber plug off of that stainless pipe to look at it while the unit is running will tell you if there's a leak there or not. The way you describe your water volume in the bilge I do not suspect this is the problem but I'm wondering if it could be how some of the water is getting into your previous Motors? Might never know since you are swapping out the motor but make sure that O-ring is there if you ever rebuild one for some reason during this journey.
Another way that we test waverunners for leaks is to actually fill the bilge up with water and then we put the nose High on dry land to check for where water might be coming out of the boat. Missing O-rings around the drain plug holes, water coming out through the actual transom plates, and definitely water coming out through the broken black rubber donut on those intermediate shaft bearing housings is commonly found by doing this. When you're on land, your Motors are completely sealed front to back all the way up to the bottom of your airbox cover. I wouldn't go that far as far as adding water to your bilge however if you just filled it up so that the intermediate shaft bearing housing has water at least halfway or 3/4 of the way up that should be enough to find any leaks running backwards?
At the end of the day this is probably a lot of useless information that you've already covered and I get that. I just wanted to throw some other things out there in case it can help.