with proper context, it sounds like you want to maintain trainer details of the save, stuff like that. maybe the new conversion will make up in game story flags or something, I dunno. The answer to direct save conversion is no.
However, let's look at the points you mentioned
You can do that with third party tools
proper transfer tools don't change the Pokemon's OT.
The Pokemon will stay 'legal' as long as the transfer isn't into a Switch game
(Even into Switch games, the data is technically legal, but the issue would be the lack of a legal HOME tracker)
If your Pokemon file already has a HOME tracker, we are able to transfer it over to different saves and create official movesets matching the game, no problems there.
Once again, the focus shouldn't be 'transferring saves across different games'. So many details goes into the saves which are pointless in other games.
The question (or rather this mentality) is either misleading, or is a real problem.
Anyhow, transferring mons across games cause you love them, and want to preserve them? Not an issue!
(Note: this is only true if the species exists in the receiving game)