Some previous owner glued thin wood strips to the bathroom walls with
an adhesive. This has been falling off for years. I want to replace
it with clean painted walls. I have been trying to remove the
adhesive but continue to accidentally gouge the drywall in the
process.

The ceiling is fine shape. If I tear down all the drywall on the
walls, will I be able to get a good seam with the existing ceiling? I
know I would tape and mud the joint, but there will already be tape
and mud on the ceiling from the previous joint.