The whole thing with cave-ins is one of the many reasons why I'm glad it's not ME programming this game. I woudln't know where to start... you don't want to allow ridiculous constructions, (I once built an aqueduct with no supports) and yet you don't want the mining to go super-slow while it checks for everything.
I don't fully understand your idea here, but if the cave-in checks are a localized thing, then perhaps they won't take up so much processing power after all. On the other hand, every time I channel upwards with ramps, the game lags like hell trying to determine what it should do with the other ramps in a tiny 3x3 square.
My only comment would be that I think it should be a bit more lenient than 7x7. Already, we have natural caverns which exceed 7x7:

When I first saw the caverns, I got the impression that Toady was going to be more generous when the time came to add the cave-ins.
Obviously, we wouldn't want for such a thing to cave in on embark. And you wouldn't want it to be artificially supported with a kind of "if the terrain exists already, it will not collapse" type of thing. -- you're saying that a multi-level domed ceiling would prevent this? I guess that makes sense - however, it would also allow atrocities like this:

Seems like you'd need a bit more code. I have no idea what that'd be, though...
EDIT: Actually, I just got an idea. Perhaps, every single solid tile would have two variables - compressive strength and tensile strength. As you mine beneath something, these variables are deducted from until one of them reaches zero. Then, perhaps after a warning, the structure would collapse.
In my silly picture above, the problem is not compressive strength, but rather TENSILE strength. Alternatively, if you have a heavy thing perfectly balanced on a single tile, but that tile is made from soap or dirt or something, it would be the compressive strength variable that would reach zero.
This system would NOT work without a brilliant and simple way to know which tiles should be receiving which deductions, however... a system which I doubt could ever exist...