I’m not 100% sure but the 2nd thing sounds a lot like what I provided so maybe what I did will help. Essentially it was just a short paragraph on official letterhead from a client saying “this is who we are, this is what we have hired justin for in the past, we intent to continue to hire him a a freelancer/remote worker.” Maybe I am misunderstanding your problem but I wonder if they would be happier with you just putting this on your own official letterhead.
That said, I also had a situation where I had to explain to them why I could not provide exactly what they were asking for and they seemed fine with it.
For example telling them your intended travel dates but also letting them know you are waiting for approval before you buy your ticket.
In my experience they were pretty understanding about stuff like that.