+xBest option would be something like G10 fiberglass sheet used to make ramps/wedges that fair the tubes into the tube. Since you are not vacuum bagging, you'll have to keep the whole thing convex to get pressure from your shrink tape. You could also use epoxy and high-density filler / milled fibers to cast a ramp in place using a stick and some packing tape to get a nice surface. It would be ok to tack the tubes in place with some 5-minute epoxy or something before casting in any filler - just so things don't move.
Not sure of the load situation but if its just tension - pulling the bushing off the tube - and no twisting on the tube it should be ok. Maybe cut a few of your woven plies so the fiber is running +/-45 to the uni hoop. It wouldn't be a bad idea to lap some of these outer plies of carbon onto the tube covering the inside band. The band may not have to be a consistent width like the old one - and more bonding area is good.
Excellent ideas thanks Chris, I'm at home using epoxy filler for fairing so if I pick up some high density that may be my preference, good tip about creating bonding area from the outer layers all the way to the tube, I hadn't thought about that and the finish will be painted so I'm not aiming for amazing carbon looks, better to aim for strong bonds! The loading is very much tension only, the tube becomes a crane arm, this bracket is the attachment point to hold the crane arm up at 90 degrees and attach the 3:1 lifting tackle to the load on the lower side.
Thanks for thinking this through!