Pheromone vaporizators work wonders. Just make sure to pre-emptively set it up like 2 weeks prior. Not magic, but helps massively in my experience. Might help with your resident cat's anxiety long term, too.

I would not under any circumstances do the introduction of a new cat during a move or shortly after, as you said, it will just add to the stress of the resident cat and prolong the process needlessly.

On top of that, best way I have found is have the kitten in one room, and every day introduce the kitten's smell to the new cat. Smells are incredibly important for cats.

Take it slow, do short controlled "shows" for the resident cat, show the kitten far away, don't let it too close too quickly, that's when defense kicks in and it prolongs the process.

Overall, be patient, go slow, don't force interactions, pay close mind to body language. Majority of cats will get a long as long as the introduction is done properly, and on their terms. How long it takes is highly dependent on the individual cats and their tempers. From your post, it could be on the longer end of the spectrum.

Have a worst case scenario planned out before making any choices. If it seems like there's no way, you will have to accept that as well, and be ready to rehome the kitten.

This is a good video about the subject: https://youtu.be/tsYT7yIOdqQ Jackson Galaxy is a weird dude, but he does know cats.