Popped drywall tape - textured ceiling

40yr old house. A 6-8 ft length of tape has lifted on a textured ceiling in a bedroom - not popcorn, more a med grit sand type finish. The tape is sitting there, texture is still adhered. When I tap it with a finger I can see the tape is loose. The tape is lying fully flat, no ridge or anything.

I'd hate to replace just this strip as I'd never be able to match the surrounding texture.

I can get a utility knife tip just under the tape edge to gently lift. Is it feasible to inject (syringe, etc.) a clear adhesive into or under the tape?

A small test near the wall did flake a bit of the brittle texture coat...guessing this does not bode well for a clean repair.

Suggestions?