All good points.
And I’d argue a bit of the opposite.
I think that if you 1. figured this horse out once, you can do it again; 2. if the new place has a round pen or somewhere similarly safe and quiet that you can take ride him if he has a set back; it will be OK.
You have built a foundation that you can come back to. IMO, horses need to learn to be rideable anywhere and any time. So think of this move as giving you the opportunity to solidify the foundation you built. And it will give him confidence in you and in himself to discover that your ride has not changed in the new, chaotic place. You may not be working on jumping larger fences, but OMG you are working on making him a useful horse. And don’t let anyone tell you that a horse that can jump bigger (in theory) but becomes unthinking and hard to ride at shows is a good thing.
All that is to say: Move him whenever you want (or really, when you find the next place that will offer him care at least as good as what he gets now, plus some extra things you want), and then commit to “training the horse you have” when you get there.
I know this because I did this with a very hot mare I bought several years ago. She has great focus and teachability now, but used to be the horse that might spin you off on the trail and was down-right dangerous with cattle. Her job title is Dressage Horse. But what has been most important for making her able to do that job in a way that’s worth taking to a horse show is the Everything Else I had to teach her.
So, for example, if your horse needs drugs to get into a trailer, you need to get access to a trailer you can use to teach him to load. And that job is as valuable as something like a good flying change. Just teach him what he needs to know and that he can be safe if he takes direction from you in whatever situation you find yourself in.
But, yes, the recipe of New Place plus Crispy Fall Weather might make your job harder than it would be otherwise, LOL.