How to hang cabinets on a curved wall?

Ok, so I decided to build some hanging bookcases for my basement; hanging, since a desktop will soon (!) be constructed below it.

The cabinets are made of 3/4" maple plywood, 24" wide, 31" high, and

11 3/4" deep, all outside measurements. There will be 6 of them across the wall, with a 30" (or so, not sure yet) floor standing bookcase that will match the other book cases in height.

Bookcases are standard box construction, biscuit joined with a faceframe to be applied after they're mounted. The back has a groove deep enough for a 1/4" back and a 3/4" 45 degree plywood hanger. The matching 45 degree hanger is of course screwed to the wall studs.

The problem is this: there is a section of the wall that bows out about 1/4" to 3/8" of an inch that causes the cabinets to not sit properly square to the wall. Since the cabinets are 10 3/4" deep, this leads to a gap between the cabinets at the front edge, where the face frame will be placed. In fact, as I look at it now, there's a

1/4" gap between two cabinets.

I was planning on overlapping the cabinet fronts by 1/4" on each edge with the face frame (this would make 3/4" + 3/4" + 1/2" = 2" face frame) which would cover the gap, but since the cabinets are not square, there will be a gap if you look at the cabinets closely, since the face frame will not sit flush with the front of both cabinets that are butted together.

I also wanted to screw the cabinets to each other (more strength), and to the wall. Tough to screw the cabinets together when they're not butted tight together!

So, what can I do to fix this? Near as I can tell, the only thing that I can do is to shim out the wall mount bracket until it's flat (which could get ugly, as it's a 15' wall). I would also have to shim the bottom of the cabinets to keep them plumb, but that's not a big deal as I was planning on putting in under-shelf lighting - any gaps created by plumbing the cabinets would be hidden by the box built around the lights.

What do you think? Good? Bad? Or, so you have another solution?

Many thanks.

First, try running a string line across the wall, from one side to the other at the same height your cabinets will be. This will show how wavy the wall really is. Then i would try screwing the drywall back to the studs if, when you knock on it, it seems loose against the studs. If this doesn't help you could remove the drywall from the around the bowed stud(s) in such a way that your shelves will conceal the hole. this should get you 3/8 or 1/2 inch further back. Being in the basement, there is a good possibility the studs are 24" o.c. and not the normal 16". You may also try taking a block of wood, a good hammer and carefully smacking the bowed stud back into plane with the rest of them in the area that will be covered and re-installing the drywall you cut out.- good luck -dave