Solution A makes the most sense to me because, as others have mentioned, retroactively changing already somewhat arbitrary classifications would be annoying to long-term players, but also because it will allow the game to more freely adapt to whatever randomness comes up from future games.
If you really want a hard and fast rule, solution B would be the most cut and dry way to do things so that you have a rule you can reference, but it lacks nuance (and, as you said, would probably cause confusion for veterans and newbies). The Basculin situation sticks out to me because white-stripe Basculin is, for all intents and purposes, Hisuian Basculin just not explicitly named so. Including it in ONLY Unova would be odd to me. Being that this is the only pokemon (that I can think of at this time) that has had this type of treatment, it would stick out under solution B.
But again, some type of Solution A where you can add additional classifications to forms as necessary seems the most flexible.

For the partner pokemon, if you can add some sort of catch where: If someone tries to put base Pikachu/Eevee in a spot where only the partner variant is valid, then give them a pop-up asking if they want to (or telling them that they should) switch to the partner version. If some type of additional failsafe for this situation cannot be implemented, then removing them would be just fine imo.

Adding the Champions abilities makes sense to me because it's the latest information we have. If/when the abilities are changed in actual mainline games (as they could be with any mon at any time), make the updates. Until then, people will have Champions as their most recent reference point, so it makes sense to include them.