You can also try and swap the bolt as well. There can be minor variables to the bolt length, which can effect the headspace. There are also variations in the thickness of the various boltheads, even with the same number.
If neither of these clears up the problem, and the rifle is nothing special, then you are in for some tough choices. It is not cost effective to have the barrel set back, but you could always find a sporterised donor rifle and replace the receiver and bolt. Often these sporterised rifles can be had at a bargain. I just picked up two, one a savage and one a matched LB, for $40 each.
An article I read a bunch of years back mentioned the danger of forcing a Enfield closed onto a no-go guage. It estimated the force at the bolthead in the range of 18,000 pounds thanks to the leverage of the bolt handle. That kind of force can ruin the bolt or receiver in a hurry.