Do it right, do it once. Take down drywall, insulate with batts or foam and redo drywall.
***** but no easy way out.
^^^ ... and depending on where you live consider installing a vapour barrier.
Leave the drywall where it is, and use dense pack cellulose.
You drill two holes in the board, one on top, one lower down. You need a stronger machine than the free ones you get, has to put out at least 3 psi.
A dense pack wall will also control air leaks, while having equal R-value of fiberglass.