If I cut out a 20 second chunk from each track, starting from about 1:25, using Audacity, would it negatively affect the samples at all? I want to be able to easily play the same chunk of music from each track quickly back and forth.
No, nothing wrong with doing that. Of course it's also possible to use Audacity to cheat, but you won't do that, right?
As for identifying 15 second segments of one track. I can do that. In fact I was flipping between bit-depths as I was preparing the test. I could identify 8 and 12-bit, but 16-, 20-, and 24-bit all sounded the same to me. I'm just not that sure of how good a test it would be. It's hard to say, "this is 16-bit," without having something to compare against.