Congratulations on the Wireless!

You're gonna love it.
I agree that those codes are unlikely to be related to your stalling symptom. If you want, you can narrow down that P0300 by going into scan data and checking the Misfire Data list. It'll keep a history of misfires on each cylinder. Follow the one(s) with the highest counts first. What was the O2 code, specifically?
Back to the stalling. I think the simplest way to attack this is to find out what you're missing after the engine shuts off, once it turns into a no start. This has the coils right up front, so spark testing is a cinch. You can even do the patented ScannerDanner Type 2 coil test.
You can also get to the fuel injectors on this one (as opposed to the 3.1/3.4), and use a good ol' incandescent test light to look for pulse (or a noid light if you have one). If you're missing one or the other, then I'd suspect an input problem. If you have both spark and injection pulse, then I'd suspect a lack of fuel pressure. That's our diagnostic 'fork in the road'.
Also, your symptoms remind me of a two-part series Paul did on another GM with a 3.8, check it out: