GunSails make mast/sail bags. I fit 3 masts/sails.
Two separate bags, and the sail bag sits on top of the mast bag. All the fixtures are well though through, so you don't press the sails with straps.
Pretty much does what Mark said above out-of-the-box.
The price was very acceptable.
I ordered mine from Brisbane a few years ago, but that shop has closed. Not sure if someone stills supply GunSails equipment in Australia.
gunsails.com/en/windsurfgear/bags/surf-bags/?SID=o3n73b1k1uh561su12u08nro76 and
www.gunsails.com/gear/bags/surf-bags/sessionbag-1155.html