So after asking around on TCRF, a member informed me that the BAM files are actually containers for another 3DS model format: CGFX or BCH. These files are viewable in Ohana3DS Rebirth, but the BAM container itself is not. You have to extract the CGFX/BCH from the BAM file.
I managed to extract them by deleting everything before the CGFX string in the file using a hex editor, but there's probably an easier way to do this that I don't know of. My extraction method might not work for all of the BAM files, but it definitely works for a good number of them.
Maybe someone who's familiar with Every File Explorer could make a plugin for these files, if there isn't one already.