Ok....
Homebrew01: The ACTUAL problem is that the inner tube loses air pressure to the point that I'm riding on the rim. The first tube took about an hour to deflate. This new tire took about 20 minutes. Thanks anyway.
fietsbob: As I mentioned, I checked the tire and the wheel rim, and there is nothing sticking through either the tire or the rim strip that can be seen or felt on either one.
IthaDan: Same as above. Thanks for the tip about lining up the tube and tire though, that is a good idea!
If it had been any of these simple things, I know to look for them. Everyone does. That's why I'm so perplexed as to what keeps happening. It just doesn't make much sense...
I think the original tube that came with the bike must've lasted 4 years, and the one I replaced it with another 2+... Are Slime tubes really crappy or something? I thought I had used them before with good results...
Anyone have any other suggestions?