I'll reply to myself: the Roland Octa-Capture works well with MSRS. It's a bit pricier than the M-Audio FastTrack Ultra, and a bit bigger, but it has 8 XLR inputs instead of 4, and it works.
The reason it works is that Windows sees it as 4 different devices each with 2 channels, instead of one single device with 8 channels like the M-Audio. So it bypasses the problem entirely.
Just in case this info is useful to anyone...