RE: Choke tubes????
Can't help ya in the 2 3/4" range, but I have had two Remington 1187's that both liked a extended choke in the Hastings variety. The short barrel (23) liked a bit tighter constriction at .650 than did the longer barrel (28) did with the .665. Both these chokes patterened HV #6 shot very well.
You say that you tried many combinations... so what exactly have you tried? Post some patterns... would help to see what your gun is trying to do with what you've already sent down range.