"3. Also referencing the above photo, you can see the stud is recessed a bit from the chimney wall, so we have the option of butting the drywall up to the chimney and having it exposed if we like. Thoughts on that? "

Or sister the studs forward with some 2x4 halves to make a plane that allows the drywall to cover the masonry.

Your choice about appearance vs loosing floor area.
if you want to cover the brick with minimal floor loss you could just push the drywall about 1/2 inch forward of the bricks face, knock off any lumps of mortar, then plaster the brick (a bonding agent will stick well enough).

If the place is old and not subject to shifting you may be to able to forgo corner bead.

The only other way may be to strip off the texture, use narrow corner bead, and then re-texture the area you just removed after finishing the drywall.

Corner bead doe not fasten to brick all that well either, though buried in plaster would likely be adequate.

you also do not need to use old style plaster, Easysand or Durabond would be more than adequate.
When mixed with minimal water to about peanut butter consistency it barely shrinks in even thick and wide applications.

I have used it to fill in plaster grounds that had to be removed.

1.5 inches wide and 3/4 inch thick areas many feet long.

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Thanks brickeyee. Has everyone else gone AWOL?

While I'm a newbie at old houses, here's what we would try.
Put a piece of inside corner molding (or something nicer, perhaps a column of some type) for the transition between flat and the moonscape plaster. I'd also think seriously about leaving the brick exposed. I know it's not historically correct, but is really in now.

As for the corner cabinet...put it back. To repair the wall, try a flat knife blade to remove the excess caulk and paint. Patch any divots with spackle and repaint.

Hmmmmm ....

One easy solution would be to have a shallow corner "pillar" of molding and match the door jamb molding to it. A common interior detail was a "plate rail" height molding running around the room several inches below the ceiling, level with the top molding of the doors.

Use it as a gallery wall and no one will notice.

A more ambitious but still DIY project would be to build a shallow divider pillar and bookcase faux divider. Except flush with the wall, not really dividing anything.

Here is a link that might be useful: Bookcase and pillar divider wall

1. Corner molding. That was my first thought. Add it to the other side as well for symmetry.

2. Molding again. Maybe consider crown in the whole room.

3. What Mary said. I would only put the cabinet back if it was original though.

4. I'd add horizontal strips back on the studs to bring it out even with thr chimney. Then I would cover it all with drywall. I would not leave the chimney exposed.

The corner cabinet was not original. it was added when the paneled wall was replaced, probably in the 50's at the same time they put in the pink tub.

The wood from the paneling and corner cabinet looks similar to the kitchen cabinets: same color under the paint. Could those cabinets be a 50's remodel too?

I like the idea of "flat pillars" in the corners. I'm thinking 1x4s with simple trim at ceiling and floor or something. Shallow bookcases are a potential option (corner colonnade?), but I'll need to see if what that does to the floor space.

I thought someone said crown molding wasn't period accurate. True?

Crown molding wouldn't be right for the modest nature of your house, but picture molding would be, and might serve the same purpose. How high are your ceilings? I've forgotten. Anyway, in at least two of our former old houses, the picture molding was set several inches down from the ceiling. But you could also make it nearly flush, as long as there's room to ge the hook between it and the ceiling.

Right, heavy crown would not be correct, but I think you can do cove molding. Our modest 1920 foursquare had cove molding in all the rooms. In a couple of the rooms there was also a picture rail hung about six inches from the ceiling. You could do something like that.

You could also do only a picture rail as chibimimi has suggested and carry the ceiling paint color down the wall to the molding. That might help minimize the gap where the wall meets the ceiling.

You could also do something like this where it is a crown.picture rail combo.

I've worked on several 1910-1930s modest houses and most of them had a crown molding ... but it was modest sized molding. It's a good way to mask any wibbles in the wall-ceiling joints.

The one that didn't had your heavy textured plaster and coved ceilings.

And many of them also had a picture rail several inches to as much as a foot below the crown, with the wall color stopping at the picture rail molding and the ceiling color above it.