To me, it looks "do-able." I said "LOOKS." I say this because our driveway is behind our house and the alley leading to it is maybe 18' wide, if that. I have to make a hard 90-degree turn to back into the driveway (the paved part of which is only 9' wide) to park it. That said - my trailer is 2' shorter than yours and my TV wheelbase is just over 10'. Hitch to ball distance is about the same as yours, maybe a bit shorter. I do cut across some of the grass on the inside of the turn - it's unavoidable.
My concern would be this - if your across the street neighbors are as ornery as you say, I can easily see the wife parking her car closer to the alley to prevent you from having enough room to swing the front end of your TV around - simply to be a pain and/or precipitate a confrontation. Other than that, I agree with both of the above replies to your post. Good luck and let us know how it turns out.