Following my overly personal TMI post, I came to a conclusion:
The slippy straps were slippy because they're made of fabric and not elastic. Elastic has gripper qualities that smooth fabrics don't have, so that was the problem. The exploding bra had elastic straps, so they stayed up better.
Following the advice of a couple of the commenters, I went to Nordstroms over the weekend and received some terrific help with my strapitude challenges. All is now well in TMI Land.