This is all totally reasonable, but I can see how leading with this might give off a little bit of a high maintenance vibe. (Even though it sounds like you’re really the opposite!) An intro that’s basically “Hi, I’m an adult former eventer getting back in the saddle, I want to try hunters” might be an easy conversation starter.
A couple of things I might gloss over in the introduction phase if I were you, because I don’t think they’re actually of much consequence once you find a trainer and could instead lead to a needless hang up:
1 - Specific timeline on lessons vs. leasing. It’ll probably work out to take a few months from getting a couple lessons in with a trainer to finding you an actual lease horse, and a trainer might think you’re really a lesson-only client dreaming of the prospect of leasing even though it’s out of your budget or true interest.
2 - Buying a horse, ever. Life is long, you never know!
3 - Relocating in a few years. It’s is a totally fine chunk of time to be with one trainer, but I wouldn’t sell yourself as a short term client from the get go. Nobody will be mad if you move in 3 years and didn’t tell them your plans now.
I think you’re actually a totally normal client for many H/J barns, at least in my experience. Coming back from a long break, want to ride a few days a week, lease, show a little, have a good time - you’d fit right into the adult ammy group of many barns I know. (But they’re on the west coast, sorry!)
Also, waiting lists are a good sign! Join them! Sometimes they turn over quickly for no particular reason.