Hunter Arms used a full length lug for the larger BTFEs and a shorter lug in a milled grove for the skeet style BTFEs. Images are on p. 423 of Houchins.
Here's the Fox version
Winchester M21, which was adjustable
"Baker Perfect Grip"
BTW: Several variants of the "Reinforcing Wedge" or "Barrel Loop Support" are shown about 1/2 way down here, and were usually found on barrels fitted with a BTFE and also LRWF