The second post in this thread has a whole bunch of info, can't tell from your questions if you've read it or not but might as well throw it out there.
If you're playing with [SPEED:0], which you damn well should be for this sort of thing, seven-ish miners isn't so bad. I mean, sure, more often go faster, but at that speed the real-time difference isn't that wide of a margin. When you have more than 12-14, though, it's just excessive. Too many miners can dig out all the dirt around each other, which causes them to pathfind en masse back to the northwestern-most area to start again rather than take a step to the side and keep going. Really it's just important to try and keep them out of each others' paths.
In terms of the cavern, I'll list the ups/downs of each method. I only had two cave-in accidents in all of Undergrotto (ramping under a tree stupidly and accidentally deconstructing a support that I didn't think was a support) so generally as long as you're careful you shouldn't have trouble.
The main problem with this is that you have to leave access stairwells between floors, which causes your miners to waste probably 7/10 or something of their time on the job running back and forth between their mining spot and the stairwell since they will want to change floors every time they decide to dig elsewhere. If you designate everything at once you can just slowly add to the access stairwell one level at a time as they finish each level to avoid that problem, but then your issue becomes regular access: If you have ramps between levels for the final product, unless you leave out designating them to the end your miners will be able to sidestep your controlled stairwell access. You could use a different method for the levels that dwarves will be walking around and then using this method for the purely open-air levels, but then you have to worry about killing everyone below when you collapse it, so it's not so handy there. Also collapsed floors will destroy your pretty natural ramps, and it's not fun designating channels above your ramps on every single level in order to protect them. All you have to do when you're done is channel out all supporting tiles on each level, which doesn't take too long, and then get rid of the access stairwell and clear out your dwarves. Avoiding cave-ins isn't really an issue because you're kind of going that direction. It's also very unlikely you'll accidentally cause them.
I used this method to carve out the bottom half of the main cavern, but I wish I hadn't, because I ruined my ramps. Also pathfinding was hell.
This is the most arduous method and also the one I recommend. IMO it's absolutely worth it if you have the patience. Areas that will eventually become flat, designate as up-stairs. Ramps can be designated as ramps, but remember to leave undesignated squares above them. And everything else is up/down stairs. The main pro to this is obviously access, as you basically have flying dwarves. Plus if you want to do anything crazy like smooth and engrave the whole cavern it works really well. The obvious downside is that you have to channel everything away from the top down, which effectively means you have to designate everything twice, but for access purposes it's unbeatable so I think it's worth it. To avoid cave-ins, you just have to channel out all the stairs directly above all the ramps; if you don't do this, there's a pretty good chance that the dwarves will channel out a layer from below and leave the stairs directly above the ramps floating there, and ka-boom. You really just have to be careful that nobody tantrums on the stairs, since if your dwarves fall or trip or something, it's a long way down.
I used this method to carve out the top half of the main cavern. It worked really well, but because I'd already dug out and populated the bottom half, I had to leave a layer of up-stairs halfway through the cavern and slowly channel them out one at a time, which took forever. That was my own fault though, so I still recommend this method.
This method is generally pretty terrible for this sort of project. For one thing, you can't designate everything at once, which for planning purposes is absolutely necessary. You're also really likely to mess up and accidentally carve out more than you should by ramping below a ceiling you wanted to keep. I've used this a lot, and if you really want to the trick is to use regular dig designations at the edges of the ramping area as your cavern opens up downwards. It's a huge pain in the ass to remember, too. There are numerous other downsides to this, too, like the fact that ramp-carving is way more laggy than other dig methods, and the likelihood of causing cave-ins through easy mistakes. I also need to stress again that you never dig out more than one floor at a time with this no matter what, since that's a good way to kill some of your miners. There are also a lot of rules to using ramps and you might cut off your miners from food, booze, and beds if you're not familiar with them. There are up-sides to this, though; generally it's pretty easy for digging out small rooms two or three z-levels high, or digging small pits.
I used this method for hollowing out Mountaingate. It worked pretty well I guess, but in hindsight I should've done the stairs thing. I'm lucky I didn't ruin one of my circle layers with it.
Man I write way too much :\
Someone, get a god damn wiki page on this now!
Haha, I doubt that'll happen. But come to think of it, it might be a good idea for me to go make a user profile or whatever and stick all my digging advice up there. Probably easier to refer people to there than type it all up again.
Edit:
I did!