You have a "bath tub", seen as your cockpit - the area where all your seating surfaces are. You have an outer hull. The two are mated up and fastened together during assembly with some sort of adhesive. Between the inner bath tub and the outer hull is going to be a large space where water will collect due to various reasons. See the link to
@Julian's post for tracking down the multiple areas that water can find its way into your boat.
All of that info above means that the bath tub is NOT the lowest part of the boat, and the bilge pump is therefore not at the optimal point to remove all water in the boat, and will start to operate when the water fills up enough to reach the bilge pump in the engine compartment. Movement will make the water slosh around. Getting the boat up and on plane will cause the water to flow back towards the transom, at which point it will likely be pumped out by the bilge until it falls below that level. When you come off plane, the water moves forward, as these boats have a forward lean, for lack of a better term. When this happens, the water will then likely flow into the ski locker.
All of the water that is draining out is what's left between the two layers of the boat. There are MANY places the boat can take on water, and you will need to go through that thread to start to narrow down all the places you are having water coming in. There are the easy (and typical) places to start with investigating. To me, it sounds like every typical leaky Yamaha. If I were in your position (and I have been), I would start with the easiest and most vital thing - the scupper valve. If that's leaking, there's likely 90% of your issue solved. You CANNOT simply eyeball it and decide that it's fine because you don't see a crack. If it's plastic (and it likely is), it may only flex while underway, and allow water in. To check this, you will need to physically manipulate the hose and scupper to check it. There's more than a few threads here to check that out.
The next large item that's easy to check is the cleanout tray. Fill it with a garden hose and remove the inspection hatch to see if there is water leaking into the bilge. If that is indeed the case, the quick and easy fix for that is to caulk around the cleanout tray, and retest it until it doesn't leak. I would use some easy-to-remove caulk, perhaps something like weatherizing removable caulk, unless you're happy with that as a solution. The removable caulk will allow you to test it out, and address it later, after you've ruled out a few other items.
Now fill the cupholders on the swim deck. If you see them draining out somewhere, great, they're working. If you don't see any water coming out onto the swim deck anywhere, that sucks. Every time you come off plane, those will fill, and dump the water directly into your bilge.
The final easy thing to check is your anchor locker. Look for multiple threads around here to see what a crappy fitting looks like, and compare it to what yours looks like. If that needs fixing, follow those threads.
Those things are all the easy things to address. There are others, but those are the quick and dirty items that could be responsible for 95% of your water. You also may not have gotten all the water out of the boat, even with it running 5+ minutes. Jack up the front end before each item so you know you're starting with the least amount of water.
The intermediate bearing is the other big leaker, but to read your explanation, it sounds like one (or more) of the four things I mentioned is the culprit at this point, although anything is possible. If you've made it this far into this post, I"ve got bad news for you, there's lots more reading in that link above to try to track down all the places water can get in. The good news is, none of this is terribly difficult, and that link will point you to directions, threads, and pics of how to tackle your potential issues.
You can check all the things I mentioned while on the water, anchored at a sandbar, but I would NOT check the scupper while on the water. That is one item that I would simply order a stainless steel scupper for, and swap it out, no matter if it is broken or not. It WILL eventually fail on you, if it hasn't already (and is contributing to your issues).
Stop taking your boat to the questionable mechanic too LOL