One thing to remember when running the motor in some kind of container, I use a 96 gal trash can, is to not let it run too long. After 10ish minutes or so the water starts to heat up from the exhaust but I also think it's the best way to flush the motor.
I'm curious why you say " fuses take too long to blow - the damage will be done before the fuse "opens" the circuit." If the proper capacity fuse is installed why would there be damage done before the fuse blows.
What are you using now? How has the battery worked for you? I say you can never have too much battery capacity as long as you have enough room and can handle the weight of a larger battery.
I just went thru the exact same thing with my 2018 F150. Batteries charged, motor just clicks when trying to start or try to tilt motor and battery voltage measured at the pos cable on the starter drops to 3 to 4 volts. Long story short after spending 5 or 6 hours of troubleshooting over several...
What condition was the old impeller in? Was it missing any chunks of rubber? Can you run the motor in a tank or trash can, making sure the water level is above the water pump level? Try shoving a piece of wire up the pisser hole.