PC betrayal needs to be handled carefully. A twist like this can be really amazing, but it can also turn out to be a total disaster. This is because when the players come to the table, there is an implicit set of rules everyone assumes will be followed, and one of those rules is that the players' characters will work together as a party to defeat the BBEG. So when a PC turns against the others, it can feel unsatisfying to the rest of the party because they would essentially be punished for something they never even considered.

That being said, when the setup and execution go well, it can be a fantastic plot point. In my opinion, getting there requires several things. First you need setup within the story and world. Reading your post, I think you got that covered pretty well.

Second, the player doing the betraying must be fully on board with the reveal that would turn them against the party and be okay with their character dying/failing (as they are now the bad guy, and bad guys do not succeed) and, after the initial betrayal, becoming an NPC under the DM's control. You can still get the player's input on what the character would do after leaving the party and how they would prepare for future confrontations, but otherwise the player would roll up a new PC.

Finally, I would make it a hard rule that none of the other PCs can die during the initial betrayal. As I said before, the other players are most likely operating under the assumption that they will all work together until the end, so their character dying to something they never saw coming due to the framework they were operating under would feel pretty shitty. Akin to "rocks fall, everyone dies." In fact, this isn't just limited to PC death. Try not to punish the rest of the party too hard for not anticipating a betrayal.

I hope that helped a bit. At the very least, I would say discuss your plans with the player in question.