If you get a sendero contour steel barrel, and have LRI flute it with they're "type x" fluting, you will be close to the same weight as a carbon barrel of the same contour, for a little less money, but not a ton less. This is one option to do with your current barrel, though if it's shooting, I would probably just leave it alone, but that is up to you, having LRI do their thing to it may make no difference. Maybe call them and talk about it. I haven't heard of anyone that will wrap your barrel for you, though I'm sure someone will?
When you talk to some experienced precision rifle gunsmiths, many of them will tell you that carbon barrels start to walk or open up groups after they warm up. Many good smith's believe this has to do with the way they are made, most manufacturers do the rifling prior to wrapping the barrels, this induces some stress into the barrel during the wrapping process. For a hunting rifle, this common quirk often doesn't matter, as only a couple shots are generally fired anyway. To my knowledge, Bartlien is the only one doing it like it should be, they bore the barrel, then turn them down, wrap them, allow the resin to cure, then contour them, and finally, they now finish bore, single point cut the rifling, and finish lap the barrels. They creates a more stress free barrel by design.
This is just from my reading, my first hand experience is limited to a couple carbon barrels, a carbon six and a proof, the carbon six was picky, could have been many causes, but shot good with it's preferred load, but did seem to open up after a few rounds. The proof I never shot enough to warm it up, I was pretty careful with it. I have a Bartlien barrel on order now, so plan on testing it a little, but it will be a bigger 30 cal, so I'm not going to be too mean to it.
For me personally, the reason for carbon wrap is to get a sub 3 lb barrel that has a large enough muzzle diameter to thread 5/8x24 and have a solid shoulder to mount a supressor on. If ultimate light weight was the goal, I would get a #1 or #2 contour steel barrel and be lighter than any contour carbon barrel of the same length.