How should I retape an inside drywall corner when the wall is heavily textured?
If the tape on the wall is fine, one option is to cut the existing tape along the seam between the ceiling and the wall. Remove the half from the  ceiling as repair ceiling as needed.

Then, to finish, run a bead of caulk along the seam and paint. 

Tape is always preferred, but I've used caulk for inside corners in lieu of tape many times and (knock on wood) it's worked just fine for me.