Criterion is currently getting a No.4 barrel ready for market, after which they've started on the No.1 SMLE barrel. I have dropped off MLE take-off ("heavy barrel") which has the earlier knox (sp) form and the heavier contour, which like yours was shot out. Here's their web site and contact information. I agree, the heavy barrel would be more suited for the BSA, but a lot of them were re-barreled with the later SMLE barrels as well.

http://criterionbarrels.com/