Seems my program only dumped "Gym Leader Castle" registered teams. For some reason I did find the correct Pokérus byte and caught data bytes, but didn't update the file structure (neither here or in the main.c file), but pk2 dumps should be correct.
Thanks @ShadowMario3 for the detailed teams structure. Pkhex now supports all stadium savefiles, including registered teams, but I tested it earlier and seems to have some bugs (I tested registering a celebi, then dumping and the dumped file became japanese somehow).
I'll post an issue in pkhex's github, for now I've updated the dumper code to dump all registered teams, both in sk2 (direct dump pkhex compatible) and pk2 file format.
EDIT: seems the bug in pkhex was related to importing sk2 files when it couldn't decide if the file was jap or international (OT and Name both being lesd than 5 characters). Seems it is already fixed at github.