Was going to comment that but
Worldie beat me to it. But I'll expand on my thought a little:
The Origin Mark is not meant to be an in-world thing, it's a meta mechanic simply to denote what game a Pokemon is from. The reason for this is, as far as I can tell, is mostly competitive where they can choose to include or exclude Pokemon of certain origin marks (or rather for early cycle competitions focus on the current gen and then later comps allow for foreign origin marks).
Note that the Origin Mark for SV is a Terastal crystal. That is something which Paldea and the DLC locations all have in common (I'm assuming Blueberry Academy will have something to do with Terastal, though even if it doesn't being it's the sister school of Paldea's Academy it's connected to the Terastal phenomenon that way).
Interesting idea, though once again goes against the purpose of the mark's meaning. Note
the Origin Mark also matches with the Met Location data. I think maybe what you want is something akin to the "
Fateful Encounter" flag which Event Pokemon are given. That would more match with noting the Pokemon you were given is special without obscuring what game it originated in.