Thank you for all the help guys. Unfortunately, I'm still clueless.
I went and compared the MD5 checksums for the Billy Hatcher dumps, and they're an exact match. I tried installing DIOS MIOS 2.5 and using that instead, but I could only find it on a less reputable site (Winrar said the archive had invalid authenticity information). I tried it anyway (probably a bad idea), and the console powered down at the end of the opening FMV, so I just went back to 2.6. Now I've switched to the latest USB Loader GX (r1209), and it's giving me the exact same problem as Cfg USB Loader, freezing when I first start fighting with my first egg.
If it helps, here's some more information: No disc doesn't work at all--it just gives a black screen and freezes, never showing the DIOS MIOS logo, with either loader. I'm running off a PNY 8 GB flash drive, which I freshly formatted to FAT32 in 32 KB clusters just for this (used to use it for my Wii games). Maybe that's an issue, I dunno. My system menu version is 4.3 US.
And while I said Kirby Air Ride was working fine, it seems to have started freezing or powering down (I think it's done both) at random times too, so there's definitely something I've done wrong.
Edit: Just to clarify, those problems with Kirby Air Ride started before I started mucking with everything else, so it wasn't something I broke along the way.