OK I got it to work. Unfortunately this was victim to the typical “poor documentation void.”
Swiss HAS a file manager. You can hit the Eject button at the bottom to browse memory cards and etc. On the version I had, this showed empty cards for all memory cards.
I updated Swiss. Now it shows a full memory card with all my saves. But I can’t do anything with them. Forums and websites everywhere detail that Swiss can copy and backup memory card files, the UI itself refers to that action as the capability when you browse a memory card but there’s no functionality. If I hit A on a save, nothing happens. If I hit any other button, either it changes navigation, or nothing happens. There’s no move, copy, no options anywhere that I can find.
Back to GCMM, then!
The problem I appear to encounter is its limited device support. (It hasn’t been updated in years, after all.)
It cannot back up saves to other memory cards. Bizarre limitation.
It supports the SD2SP2 and the GCLoader (supposedly) but based on some Github/forum skimming, they never actually figured out how to write to the GCLoader. Well that’s not very useful, huh?
For some reason it wasn’t reading my SD2SP2, at all. Well it’s kinda redundant with the GCLoader, so I reformatted the memory card and was then able to read the SD2SP2 in GCMM and copy my save to it, thankfully.
Problem solved! Working on getting it imported into Dolphin now.