Drywall – How to finish the edges of recessed boxes in a drywall stair wall

Looking at your wall photos, can I assume that seeing hinges on both left and right, the doors (2) meet in the middle? first we have to make some assumptions based on the yet unknown. if the walls are always dry, seasoned and pose no moisture or condensation issues, there is a couple of ways you can go ahead and finish he walls with drywall. i would consider putting a 1X6 up to a 1X10 finish pine board in the corners. This should clear the hinges. You can then install 1X3 strapping on the concrete wall with PL400 adhesive and short ramset nails or concrete screws. You can then decide if you want to install any blue moisture proof rigid insulation between the strappings. Then install a vapor barrier such as 4mil plastic over the strapping and then install drywall with 1 or 1 1/4 inch screws. You then can finish your drywall and build a neat trim at the ends onto the finish pine boards. The other alternative is to build a regular frame wall out of 2X3's or 2X4's and mount to floor and upper joists. This will allow more insulation and still allow doors to open almost fully, depending on the width of the pine trim at the corners. The wider the trim in the corners, the more fully the doors will open without being restricted by the new wall. If moisture on the walls is possible, you should really consider using Dry-loc or some suitable waterproofing before you even think about closing the concrete in behind a wall. Mold and mildew with ruin your good looking wall and potentially cause foul odors and a possible health hazard.

The normal way to do this is to install blocking between the rafters (for the ceiling drywall backer) and between the studs (for the wall backer). You don't need to toenail all of them... you can screw about half of them.

Easier from a building perspective, run full length 2x4s (or equivalent) top, middle and bottom of the wall (assuming it's under 4' -- if it's taller, then 2 middles). Run 2x4s on the underside of the rafters on 16" centers. You've probably figured out by now that this is a ton of lumber with the added non-benefit of less habitable space.

Neither of these options require bevel-ing. A tiny gap at the edge of the drywall doesn't matter.

If the underlying problem is the cutting, rent a miter saw for half a day and cut your blocking in one swoop.