I don’t recall having seen an example with the Gauntlet but please be aware POI shift is very seldom the result of an insufficiently stiff barrel. Rather, it’s usually because of the barrel tenon being inadequately supported in the receiver. That’s the place to look. Does it have at least two grub screws holding it? Are they snugly bedded into dimples in the barrel tenon? The further apart they are, the better.
For example, the QB79—the model on which the Gauntlet is based—was subject to this issue. Well, it had a sturdy barrel band that took care of it but if you had reason to remove the barrel band, it would quickly become evident. The receiver had only a single grub screw. Drilling and tapping it for a second one would pretty well cure the problem.
Having said all that, if the receiver has enough meat that you can enlarge the opening to accommodate a larger OD, by all means feel free to bond a carbon fiber sleeve to the barrel and sink the whole shebang into the receiver. That works fantastically. What you want to do is bore the receiver just slightly smaller than the carbon fiber’s OD. Then turn down the CF just enough to be a slip fit so the barrel has no opportunity to wag out at the muzzle