Well, I spent some more time reading dmesg logs and messing around in the BIOS. I enabled SR-IOV [1] and the drives appeared! I'm not entirely sure _why_ this worked, but at this point (it's been over a week of messing with this), I'm a bit tired of looking. If anyone has thoughts on why this change fixed my problem, I'd love to hear them.
Thanks, Scott [1] https://en.wikipedia.org/wiki/Single-root_input/output_virtualization