I found a fix for it on my end, which was a conflict between Wumiibo and either the 3DS OS or Pretendo's HokakuCTR plugin. Entering the Wumiibo app settings → "Toggle Wumiibo State" to set it to Disabled, worked for me.
Okay, so after having played the game a bit more to rack up some high scores and unlockable toys (Apparently I didn't play Touched all that much when I first bought it in 2014), and then thinking of how to do it the other way around, here's how to do it in reverse.
Presuming the use of FBI...
Looking it up, Super Mario Wiki explains the part about Mona Pizza as this:
"As the Nintendo 3DS no longer includes the GBA cartridge slot, the Mona Pizza souvenir cannot be unlocked when played on the 3DS or on the My Nintendo-exclusive digital download version of WarioWare: Touched!."
A...
I got this guide to work in FBI and with the European game versions, though with some changes to the procedure:
1) Open FBI, then go to TWL Nand → (accept the warning) → title → 00030004 → 5a324154 (if using the NA version; 5a324150 for the European version) → data, and copy the public.sav file...