Electrical – remove/brace two studs to fit a new regular sized breaker box

If you haven't burned to a crisp yet...BURNINATE THIS PANEL

This box is very definitely a FPE Stab-Lok, and thus needs to be burninated with extreme predjudice before it burns your house down!

I'd simply replace it outright; ordinarily, an Eaton retrofit interior would be an option, but your panel is stuffed to the gills with tandems, and since tandem GFCI/AFCI breakers are not a thing, you will need far more spaces on your new panel than will fit in a cabinet that size (a 24 circuit CH main breaker retrofit interior requires 29" of height, and you only appear to have about 24"). I would get the largest panel I can, however, to avoid having "overstuffed electrical panel" syndrome again in the future.

As a result, a bare minimum replacement for this application would be a 30 space, 100A, main breaker unit; however, I would splash out and get a 42 or 54 space, 200/225A unit and downbreaker it to 100A (either through swapping to a lower amp main or using a backfed 100A branch breaker with a hold-down as the main as not all 200A panels can accept a 100A breaker in the main breaker position).

I suggest you keep marking the centers like you've done and as each plank goes up, copy that mark to the face of the plank.

You can use painter's tape if you don't want to make marks on the planks. At minimum mark the entry and exit points of the projection of the joist across the face of the plank and make a line between them (a first order approximation). You'll hit a joist most of the time. If you want to be able to better detect a joist hit, then pre-drill holes in the planks or use partially threaded wood screws with a shank longer than your plank depth.

You may not hit a joist every time, but I really doubt that you actually need to. The screws are primarily going to hold the planks in place while the glue sets.

Concerning the weight: You're adding 1.5 lbs. per square foot.

You're adding about 12.2 cubic feet of wood to the ceiling (15'×13'×0.75"). You say it's barnwood, so I would assume something like western cedar. That's 23 lbs/ft­³ (plug in a different value from here if it's not right). So you're adding a total about 280 lbs of wood plus screws/glue. Say 300 lbs. It sounds like a lot, but it's spread over the entire ceiling which is 195 square feet. That's about 1.5 lbs. per square foot, which is approximately the same weight as the drywall itself. I'd be surprised if doubling the drywall was enough to make the ceiling collapse, but I'm an electrical engineer, not an architect; so I could easily be wrong about that. Do check with a local contractor/inspector if you're concerned about it.