I am so beside myself with this problem. I hope you can figure yours out soon.. and then.. let me know how you did it.
By having the hobby of animal behavior for so long. I sound like a beginner because I'm bored when not learning through experimentation, so subconsciously make sure I'm always in new situations, perfecting it till it's no longer a challenge (not that I'd give away a kitten after curing it, but would let it just play with its siblings, as it's no longer where I'm needed).
My whole life it seemed like no rodent ever bites. Now I'm told rats are the least likely to, yet biter rat stories abound. Maybe something's been changing.
The only reason I talk like I have a biting dilema, is that thinking this way is why I don't have the problem now. If I go to her thinking she won't bite me, she will. The moment I saw an issue, I asked "How am I training her to do this?" & did the opposite. ... had I told my little letter "That feels nice, thanks for the lovely massage. You're the boss." .... I invented/designed/made equipment/procedures that would take a book to explain .... But that's just us. I think.
I PMed someone on Rattit, but her advice wasn't applicable, because it's never easy to describe & you're always going to picture someone's life as different than if you were them. What I love about this forum is that the experts here are brilliant and friends yet completely disagree, giving opposite advice than each other (sometimes), so that there's always something to help anyone or bits to take from each, one way or the other.
If (especially since neutering is never a sure thing) he could go to a new human and place (& maybe without the security of his bro would even be best) he starts over on a reset where (before his fear of newness wears off) someone who has my style (or better, SQ's) takes advantage of the initial politeness (as he investigates what customs he should establish), grabs and runs with it (this time in the direction of hey-if-I-die-of-gangrene-how-can-I-feed-you).
If he were female, I'd take him. I don't think he nor my rat would want to spend their lives alone in cages next to each other, but I only have room for two, not four.
You might place an ad for someone to give him to (assuming he'd like the rat at the new place), either if neutering him didn't work well enough &/or you too can only afford the care costs of two. I responded to CL ad but was an unfixed male. I hope you'll keep us updated.
What's needed in each major city, is a rescue that's never too full for more, in that each person who doesn't have time/space for it could still pay the rat's rent there. That would've worked when I was a child because care costs were insignificant. Nowadays, people don't even agree on diet or medicines.
What I wanted was to adopt a rat in need, but the only time I found females, the "Have you associated with someone who gave a dirty look to an animal?" & "Write your name in blood (if you've any left) that you'll use on yourself a (plastic) samurai sword upon allowing her to get a hangnail." violated my respect of privacy. Would you tell me, when you adopted from that place, what information did they ask you to give and what did they ask you to sign?