Posible swap for my 273 Barracuda 1966

You have said a number of times, free exhaust, I am assuming you mean stock exhaust manifolds going into a free-flowing exhaust? It sounds like you want to keep that since changing would be difficult.
I would go with a 318. Exhaust ports on the 360 will probably be too big for your exhaust manifolds and leak. I had 318 manifolds on my 69 Barracuda and when I went to a 360, they would not seal because of the size difference.
If you go with a 318, your motor mounts will work, as has been stated before, same internal balance so, flywheel should work as well. Your intake should bolt up also.