Go to HASPORT and look at every available motor mount option for the Integra. That is your list of swap choices. D,B,H,F,J,K (L,M,N,O,P...)
However if you are married to the dumb LS trans than it must be a B series long block.
Would it be easy to swap a b20 into it? My b18 is on its last leg it was burning oil and coolant and then I did a head gasket and pretty much every gasket from there up fix but now its losing oil from the head I believe
I'd say stick with the B series and save some $$, Hmotorsonline.com is a legit site. Shipping to Washington probably going to cost you $$; but at least you can order the motor you want and they sell the motor mounts as well.
Do a 13B-REW. Technically still a B-series....but from Mazda.
Come to think of it, I've never heard or thought of a rotary RWD swap being done in an Integra. It would be interesting since the 13B would probably weigh about as much as the B18. Then factor in the RWD swap and extra weight in the back and you might be sitting right around 50/50 weight distribution. If anything the car would be tail heavy but that could be offset by moving things as far forward as possible, like the engine and fuel tank.