No need to replace hoses unless...
They're permeated with odor or so old they're hard and brittle. Stinky hoses don't affect toilet performance. Once you get your toilets working again, you can clean any buildup out of 'em with muriatic acid.
I think you have TWO problems...one that causes water to keep filling the bowl when the thru-hull is open...and another that's preventing the toilet from discharging.
Discharge:
My first thought was low voltage to the toilet...that's the leading cause of sluggish discharge. But you say the motors are strong. Still, I'd put a volt meter on 'em anyway to make sure they're actually getting a full 12v. Check while flushing.
If the voltage checks out ok, my money is on the tank vent. Clean out the thru-hull with a screw driver blade--or whatever works...remove the vent line from the tank and clean out the fitting and that end of the hose. Before removing the vent line from the tank, it would be a VERY good idea to open the deck pumpout fitting first to relieve any pressure.
If the vent line has permeated and requires replacement, relocating the vent thru-hull might be a very good idea if it results in a shorter straighter vent line.
Bowl flooding:
The solenoid valve in the vented loop is almost certain to be your culprit...'cuz when a toilet primes, a siphon starts...and if there's no air break in the intake line, the siphon will keep the water flowing. You should be able to see/hear whether either one is working. Even if it's not, the intake impeller should at least slow down the flow of water...if it doesn't, it's time to replace the impeller.
You'll find the manual for the toilet here:
http://www.jabsco.com/files/37010_elec_toilet.pdf