You also need to consider a vapour barrier which has to on the warm side of the insulation. Our last house had two bay windows one stacked on the other, from the outside between them they had slate outer skin behind which was some sarking and just plasterboard nailed on the vertical supports on the inside. It was bloody cold in the bedroom, I removed the PB added to the thickness of supporting stud work before filling the spaces with paper lined rock wool. The paper lining extended sideways of the width of the rock wool allowing it to be nailed to the studs to stop it sliding down, these days you would probably use batts. The whole lot was covered with a PVC vapour barrier before reattaching the PB. As far as I was aware I never had any damp issues and it was an awful lot warmer.

I suppose you could simply add studs without removing the PB, fill the spaces with batts or celutex, add a vapour barrier and re-plasterboard.

Richard