I think you might have more luck getting advice specific to Angora grooming if you wrote to a couple of Angora breeders or spinners/knitters who keep their rabbits for the fibre. Sorry, I know that’s a bit of a pain but these people tend to have pretty easy to find websites and in my experience are usually friendly and helpful when approached directly for advice. I know they don’t generally house them right, … and lots of other issues, but you just want to know about the best gentlest way to groom and I suspect the people out there who breed them and harvest and spin their hair are the ones who have the kind of information you are looking for. The spinning community might be a good place to start looking.
In the mean time, your sheering sounds like the best solution. (Since I expect it must be pretty matted at this point.) Do you know someone you trust, or could you find a vet or groomer who could do the sheering for you? That way you wouldn’t be the person immediately associated with the actual event in his mind and your bond shouldn’t suffer.
Maybe after a thorough sheering you could do something like clipping him once a week, maybe with the help of a friend? Something that could keep the hair shorter and more manageable. I know he won’t like it, but it might be easier then the brushing.
Really sorry you are both having such a rough time of it. I feel pretty sure there is a way to “pluck” painlessly though, so maybe an experienced Angora handler can give you some tips. If you get any advice that works please do post it, … always good to know and you never can tell who it may help.
Best of luck!