bad connection in there somewhere leads to not enough voltage and current.
does the starter spin the motor faster when you hook the charger to the system?
under load the motor needs more fuel.
make sure the high pressure pump is keeping rail pressure in spec.
I know nothing about your Susuki, but some motors will keep RPM down if there is a failed sensor the ECU needs to be seeing working correctly
Have you drained the lower unit lately to make sure there is no water in there?
to me it seems the level should not be that high.
where is the level plug in comparison to that boot?
you may have water in the bottom causing the level to rise
sounds to me like you cannot get the RPMS up due to VST running out of fuel if the motor will get up with no load on it.
takes more fuel under a load.
does it help any when pumping the primmer bulb?
or turn the key off as soon as the motor dies and then drain the VST to see how much fuel comes out
then follow Boscoes recommendations on numbers on parts and report back what you find, I am sure he can help with those even if you techs said they could not
I am not very familiar with that 4-stroke motor, but timing advancement and additional fuel is needed when load is applied. since you replaced the carb, I would be monitoring the timing to make sure it is in spec and advancing as it should
so it does sound like you shredded a water pump impellor, hope you found all of the pieces and they are not blocking cooing passages inside the motor.
Yamaha does not monitor oil and water pressure or flow, just oil level and water/motor temp
as far as manuals go look for the manuals part...