Problem seems to be solved
I just took the car for about an hour drive (filled it up - $51.00 dollars - ouch). Anyways, I got back home and I didn't have any exhaust smell on my clothes to speak of.
Cure - I replaced both my positive and negative batter cables. The negative appeared to be okay. The positive cable is another story. It had the GM "platic conduit" wrap around it, and detail tape in other areas. Other than the aftermarket ends, it looked okay. I tore the wrap and detail tape off, and here is what I found (keep in mind I figured out after I bought the car that someone had a huge stereo system in it at one point and had apparently modified the positive cable to run amps, leads, etc.):
Picture #1:
This was the cable going to the alternator. It 's a different grade of wire than a normal battery cable - has many, many fine lines versus heavy duty cable. Also, the fusible link on the ECM wire had been removed and the orange wire crimped right onto the connecter. You can also see a wire had been soldered into the ECM wire at some point (this was covered by detail tape).
Picture #2:
This one is even more interesting. I mentioned that aftermarket wire was used for the connection to the battery. Just a few inches below this, the wire was spliced into the original alternator wire with some sort of brass junction. This junction was covered with heat shrink, and looked very nice from the outside.
Picture #3:
Just another view from a little further back.
Picture #4:
Here is a view of the connector and wire that ran to the starter. Again, it had detail wrap all around it which made it look very nice. I took the tape off and the connecter actually fell off into my hand.
So, I am thinking this wiring was bad enough that the computer was resetting itself all the time, and chip had to continually relearn settings, causing it to run rich like it was initially starting up after a chip swap.
Thanks TurboNasty, JDPolzin, Eric, and Jay for helping out on this matter.
Rob