1992 Corvette coupe sputters when warm?

I have a 1992 Corvette coupe, automatic transmission, with somewhere over 150,000 miles on it, but I keep it perfectly maintained -- it always goes in for its 30,000 and 60,000 mile servicing, and just for extra care, I almost always take it to the dealer, even for oil changes.

A few years ago, it developed a weird sputtering problem. It happens once the car is warm; in warm weather, it's soon after it's started. The sputtering generally happens between 1500 and 2500 RPM, and tends to make the transmission shift into higher gears. When it's really bad, and I'm trying to drive around town, I can shift into second gear and that seems to reduce the problem vastly.

I've had the transmission soft-rebuilt, I've had the water pump and OptiSpark replaced, and I had a blown head gasket replaced. Nothing has helped. Right now my plan is to drive the damn thing until it completely breaks, and then see what the heck was wrong, but obviously I'd prefer to fix it before that.

Any idea what could be wrong with it? Or what to test? It never seems to happen for the mechanic.