Did the service engine soon light ever illuminate? It does noramlly come on when the engine stalls, but I mean after you start it up or when the car is running does it come on? If so you should get the codes checked at a shop. Unfortunately, your Regal is one is one of those different cars that you can't just use a jumper in the ALDL port with and you can't use an OBD-II scanner like the parts stores usually use either.
I suspect your problem is either vacuum or temperature related. Check all the vacuum hoses and make sure the air intake clamps are tight. Your coolant temp sensor (not to be confused with the temp switch/temp sending unit) may be bad causing the car to run too rich after the engine warms up.
It could also be a bad fuel pressure regulator. It's the little round part at the end of your rear fuel rail and has a vacuum line going to it. If you pull the vacuum line off and see/smell gas this part is bad.
This is a long shot, but have you ever replaced the vacuum modulator? It is located on the front of the transmission and has a vacuum line going to it. When the these fail, transmission fluid sometimes gets sucked into the vacuum line and eventually into the engine through the intake plenum. The car shifts noticably harder after these fail, but if the modulator has been bad since you've owned the car you may not notice this. A new vacuum modulator is fairly cheap at around $15.
Given the car's age, it could be a combination of these things causing problems too so keep that in mind as well.