Ok. You are not alone. I have a 2017 SX190 with the same symptoms. My own over heat conditions usually happen about 25 minutes after the boat has been started and we are under way. I have been on a quest to solve the issue and it has been elusive. To begin with I don't believe there is a crushed or weak hose that is preventing adequate cooling water (but I will keep this in mind). The evidence for this is that the engine is by passing water properly and it's not steaming or overly hot when Limp Mode arrives. The dual battery scenario above intrigues me as my 2nd battery was on its way out and bad voltage has a way of triggering all kinds of sensor issues. By the way if the late model 190s' do not have a volt meter or it's buried deep in a menu, you might consider buying an aftermarket unit and installing it. Having installed a volt meter has saved my butt twice and it's a super easy DIY.
Moving on though:
I've pulled the T-Stat and found it stuck "Open" and it was replaced. Additionally I have pulled the "Thermoswitch" and bench tested it per the Manual and it tested correctly. This switch, per the Manual is what is supposed to trigger the Overheat condition. To be on the safe side I replaced it anyway. Next I removed and replaced 1 of the "Engine Temperature Sensors" there are at least 2 of these. It also bench tested correctly but it showed rust and corrosion where the electrical leads were attached. Since the replacing these sensors I have not had the overheat alarm. However, I have not been underway for more than 25 minutes since my destinations during the winter have only been to the sandbar and back. I posted the volt meter vid and the T-Stat change on YT (links below) and the other vids for the sensor changes are in the editing stage.
Good Luck on sorting this out and post back anything that you uncover.
T-Stat Replacement Link -
Volt Meter Link -