If you are going to patch the 4" gap, you can try using a drywall
which is thinner than the existing walls (if possible). So if you
have 1/2" on your walls, use 3/8. This can make feathering in the
patch easier.

You said you had a double top-plate? Hopefully it wasn't load-bearing
- you might want to confirm. Did the builder use furring strips under
the joists? Or is the ceiling drywall attached directly to the
joists? Adding add'l furring strips is pretty easy and gives you a
nailing edge for your drywall.