The impression I get is that the deep rims + schrader valves thing is getting more popular with the newer department store bikes which are starting to be sold at the lower-mid level (~$250). The components are decent, creeping up on the lower end of the LBS territory, but I get the impression the manufacturers don't want to stray from Schrader valves, because the less-hardcore buyers find them familiar and convenient. This is exactly the type of bike that I'm having these problems with.

Anyway...

I tried the Presta tube with the metal rim adapter at 85 PSI and it flatted out on me overnight again. It was kinda weird; it was another flat in the belly of the tube, but this time it wasn't near where the valve reinforcement patch was, but about 20 degrees away from it. I'll post a photo when I have time. So just switching to Presta with some valve-tugging didn't seem to do the trick. (I wanted to try the path of least resistance first.) Back to the drawing board with the suggestions earlier in this thread...