Call them and ask them outright what they're looking for - "continuous RLE documentation" doesn't tell you what you need to know, they should have been more specific.
We could give you a ton of suggestions and ideas as to what WE think would be considered "proper documentation", but we could be totally wrong. Any examples/information from others may not help you if they don't have the same insurance (maybe different insurance companies require different things?) Only way to be 100% positive that you get what you need is to ask yours directly.
I would assume they are talking about official paper documentation though - notes from doctors, notes from a gender therapist, legal documents for name change, etc etc - and not so much "well my friends and family call me "male/female name" all the time". That's my guess, though i'm sure they want to hear that you've socially and personally transitioned as well. They want physical proof that you're transitioning and living as the gender you identify as. What constitutes that physical proof is up to them, i guess.
I've only just started looking into top surgery and my endo was the one to bring it up at my last visit. He said i should call my insurance company for a list of surgeons they cover, then talk to my hematologist about which one/s she recommends if i'm cleared by her, and then he would have to write a reference letter for both insurance and surgeon. He also mentioned my therapist would likely have to do that, as well.
I'm going to keep an eye on this because i'm curious, too - i don't see my therapist for another two weeks but when i do i'll bring it up and see what he thinks. I can post his response, if you want.