your GM dealer with a Tech2 may be the best way to go on something like this. =That's what these diagnostic machines are for.
this sounds like a CKP sensor thing. Exactly when does the engine die out, right above 1/4 on the thermostat? If the CKP has a bad sensor, the engine rpm will drop ~500rpm causing a stall while it switches then goes back.
Watch the engine temp when it gets close to 1/4, and watch for the blip in rpms = CKP sensor.
http://www.automotiveforums.com/vbul...ght=crankshaft
Remember: You can restart in neutral also (not just park).