Still can't find the answer.

I'm hopeing that someone can point me in the right direction here is the most descriptive explanation of what is going on with my car:

I have a '92 Cavalier that is having a problem with stalling after driving for a while. When you start the car up, it starts up beautifully and runs great. However after driving for about 20-25 minutes, I can tap the gas pedal lightly and if the car jerks, then I know that when I come to a complete stop, the car will jerk and then stall out. When this happens, I can start the car right back up, however when I put it in any gear, except park and neutral, the car will stall right out. I usually have to wait 10-15 minutes before I can start the car, put it in drive, and then drive off. A sorta work around that I have found is to tap the gas pedal, and if it jerks, then I just slam the gas pedal all the way down. The car will accelerate very heavily/slowly, and then acts as if something gets dislodged and then the car will accelerate normally. From this point I can come to a complete stop and the car won't stall out. It will remain this way for about 2-3 minutes and then the problem comes back. I have replaced the fuel filter and yet the problem still exists, but doesn't jerk as bad. The car has done a lot of heavy sitting, and I have ran fuel injector cleaner through it, however I haven't ran any through the tank since I replaced the fuel filter. I have also tried a bottle of iso-heat, which didn't help at all. I did have a problem with water in the fuel system about a year ago, but I have taken care of that problem by running a couple of bottles of iso-heat through the tank. So I'm not sure if that is related, but I never had the problem until just about 2-3 months ago. That is when the stalling problem started up. Thanks for your help.