My head hurts.

About half the cabinet value is in the face frame, door and drawer fronts. The other half is in the carcase. So what is the beautiful old quality that you're trying to keep?

Certainly, you can do a refacing and replace the doors and drawer fronts. Typically, the face frames are simply veneered over. Since it sounds like the original 1939 were site-built, the face frames are attached with whatever method the cabinetmaker was familiar with.

If you only need a couple more inches depth of the base cabinets, why not remove and replace the countertop, remove the bases from the wall, add a 2x4 behind them, and simply move out an inch and a half? No one will ever know that the boxes don't go all the way to the wall and you will gain the extra to insert a dishwasher, flush fit a stove, etc.

A cabinet shop should be able to make drawer boxes of whatever quality you want, from stapled together particleboard to dovetailed maple.

I'd suggest you get the book below from your library or bookstore and read it first.

Of course, I may still not understand what you are trying to accomplish.

Here is a link that might be useful: refacing kitchen cabinets

Thanks---I should clarify, the beauty (at least for us, having looked at lots of homes with Home Depot cabinets!) is in the construction of the boxes, which is rock solid. We don't mind the doors, but they are very 1940s while the rest of the house is Arts & Crafts, so we'd love to bring the kitchen back to that look and feel. The drawer boxes are failing, but if they can be easily repaired, they're fine as is in terms of the "look." (They're pretty simple construction---just plywood and nails---so nothing that necessarily needs preserving or not.) They are currently painted and will probably continue to be, so no need for veneers, etc., if we replace the doors.

Thanks---moving the cabinets in particular could be a good option, if that turns out to be feasible.

If the cabinets are built in place, it will probably be almost impossible to move them out without destroying them.

As to your plan, anything is possible. The question should be whether it's worth pursuing, and this seems unlikely. Attaching an additional layer of face-frame to the existing frame is a bad idea; you'd have to remove the old and build new. Like Bob, I am skeptical that your existing 'boxes' are so wonderful. They're too shallow, fitted with motley, mismatched hinges, and the drawers are shot. Building a face frame one inch thicker than usual means building it with lumber that's one inch thicker than typical. Thicker lumber is more expensive and, in many areas, much harder to obtain. Joining the pieces together will be trickier, and may have to be done on-site. There will be a lot of very careful measuring for the drawers, which will have to be custom-built; installing them will be a finicky process. On top of all that, you're concerned about the price. I suspect you'll find it difficult to locate a carpenter willing to do it at all, because it's slow, fussy, risky work and not very lucrative. If you succeed in finding someone, you may find the cost/benefit ratio rather high. But, hey, there's no harm in asking a few craftsmen to look at it.

If your plan doesn't pan out, you might look at local cabinet shops as an alternative to Lowes/HD.

I second jon1270's sentiments... old built-ins don't usually have much in the way of structure, other than their attachment to the walls. So removing them to move them a bit would probably be hard/expensive. Plus, your outside ends (if any) would then be gappy, so that would have to be dealt with.

If it comes to it, the hinges below might allow you to keep your not-so-beloved doors.

Here is a link that might be useful: 3/8 offset hinges