The easy answer is to not butt drywall to timbers, but to run it behind the edges. Also, I'd try to cut brace mortices at the center of the main timbers rather than hold them to the back edge, so painting and finishing is simplified.

If you have to butt sheetrock to timbers, ask your supplier for J-channel to wrap the edge of the rock [cut away the tapered edge of the sheet, or you'll see the taper]. At least one brand has a flange that extends outward to protect the timber while painting, which can be torn away afterward. If you can fasten the J to the timber but let the leg behind the drywall float, shrinkage of the timber won't open up a crack between the two [you will have to touch up the paint as the J pulls toward the edge of the rock, unless you prepaint before installing].