Start with a compression test, but since you didn't complain about performance when it does run then I'm guessing the mechanics of the engine are sound. (Also, if it doesn't use any oil then no need to rebuild the engine)
If it's not overheating just before it quits, chances are you have a sensor or other computer related issue. I believe any good MC dealer could scan your system or use an ohm meter to check each sensor to see where the problem might be.
My '93 LT-1 has a slight stumble on acceleration and also starts hard when the engine is hot, so I'm going to try a TPS (throttle position sensor) and go from there.
A '93 S & S with LT-1 is really rare, so you should try to keep the boat as stock as possible.
Is yours a powerslot trans or 1:1?
Oh and post some pics, your killing me!