First- If the motor runs perfect at start up its NOT the timing belt.
need more info now,
Was the boat running normal before the work was done?
1. did you get your therrmostat from a Lexus dealer? if so its most likely a car thermostat rated at 180 degrees which is not ok on this engine.
2. Did you remove and clean the MAF sensor? you may have installed it backwards ( i did this a few year ago it had symptoms like your having
3. Does your boat have a closed cooling system?
4. Does the throttle plate have carbon buildup around the edges?
5. did you disconnect the temp sensor by any chance?
6. you need to check for codes ( i will post how on another topic, its good info everybody should have) remember if you disconnect the battery or shut off the perko switch all codes will be erased. Run the boat until you have a problem shut it off, turn it to accessory and check for codes. they will flash like old school toyota 2 digit codes.
you said you ran it with the hose attached, are you getting water out the exhaust? can you touch the manifolds where the exhaust hoses attach once its warmed up? should be warm but able to keep your hand on them without burning you hands.