Air bubble under top crust

Take a closer look at your big bubbles.  Does it look like they follow any pattern or tend to be between dough layers as you shape the loaf?  Then shaping could be the problem.  If you use lots of flour when deflating and shaping, the dough separates easier.  The mention of "peeling off" the crust sounds like pulling apart cinnamon rolls.  There, it is the fat or fillings that separates the layers.  Try using less flour (no flour if you can) and tighter shaping techniques. 

Whether the dough is overproofed or not is up for debate.  Are you using doughs with yeast or sourdoughs?  How long and at what temperature are they proofing?  It could be a combination of underproofing and loose shape causing your caverns too.  Check out some of the shaping videos.  "Firm dough" sounds more like underproofing or too much flour in the dough, this might also prevent the dough from sticking to itself when shaping.  Does anything sound familiar?

The kids are quicker with computers.  Tip: the photo's will have to be downsized first before being accepted. 

Mini

I have had a few caves and they seem to be related to possible underdevelopment (allowing gas to flow more than it should and accumulate against the top "skin" of the dough) and loaf formation. Your description of a tight crumb seems to support possible underdevelopment and gas leakage. This seems to be more of a problem in my experience with certain breads, like Pane Pugliese (made with AP). After a couple of bouts of caves I paid more attention to the development and loaf forming and the problem went away.

Oh, yeah... Don't let it double. Bake it at about 70% expanded. You will get better results in my experience with sourdough at that point.

Let us know what you try and how it works!
Jay

What seems to work for me is to prick the top of the loaf sparingly all over with a fine skewer at the start of the proofing time. Because I do a long overnight proof in the fridge I sometimes have to prick them again in the morning if air bubbles have formed, but it sems to work and the finished product comes out fine.

I just had a loaf that did exactly that - the crumb underneath was quite dense, and the flavour wasn't so good as normal.  I checked in one of my books, and it suggested underproofing was the culprit.  When I thought about it later, I'd definitely not proofed for as long as usual after shaping.   Could this be the issue for you, too?  The other thing I discovered is that it really helps to be very gentle when folding your dough, and especially when shaping.  I noticed that sometimes the bubbles would come up to the surface of the dough when I'm shaping - now I try to be really gentle, so that they stay inside the dough, and then be careful when tipping out onto the baking sheet/stone.

Good luck!