I've often run into this, in my latest fort I'm getting around it by entirely skipping the temporary fort.
But this experiment has made me think about the problem a little bit differently. The biggest problem that I see right now is really a trade-off: The surface has soil, water, everything you need for food. It's also quickly accessible, but I don't actually think that's a big problem, because you can always get everyone who's not a miner to haul everything inside while you're digging down and carving out your fort, and your first 7 can survive without beds for a season (or you can throw together a surface carpenter's workshop and just pump out a few beds, it doesn't make much difference). Down in the deeps there's magma. Ores (the other thing I care about most) can be at a lot of different levels, but most iron ore, flux, and coal (I like steel... for obvious reasons) tend to be in sedimentary layers, near the surface. And trees for charcoal are obviously also on the surface.
The one thing, I think, that can be trickier about going straight for the depths is food and drink. You need to get farms up before too long, or you may be in trouble if you're blessed/cursed with a large initial migrant wave. Of course, I think you can survive without farming, but you have to have a steady stream of caravans. Anyway, my solution to this problem is that I bring a LOT of food and drink at embark, and I also bring 3-4 picks (more picks means that you get started faster, and the only thing that's kind of slow is flooding your farm plots... but if you prioritize that, it doesn't end up being a big problem, especially if you give yourself a big reserve at the start).
I've also had essentially two forts before. It's a bit tricky to manage efficiently, because if you're not careful you'll have dwarves running the 100+ tiles between the upper and lower fort just because they want a +cave spider silk sock+, and you can lose a lot of time to that. Burrows, careful stockpile management, things like that can help, and if you plan ahead to make sure that your two forts are separated by the minimum number of steps, that can make a big difference. It can also be FUN if you're not careful about where your military is stationed... okay, you can make that easy if you seal off the caverns, then your military can just be stationed in the upper fort... but where's the fun in that? Anyway, I've gotten that working decently well once or twice, but never really optimally. I expect that if you were really optimal about it, you could get some wins in efficiency, as your near surface dwellers could easily specialize in all of your farm production, carpentry, etc., while your deep dwarves can dedicate their lives to smithing. You need haulers to move things between the two forts, but you kind of need that anyway if you want to produce steel at magma smelters/forges (since all the supplies are located at shallow depths), so if you really do it carefully and right, I think the two forts can get you the best of both worlds. So I think that's another approach to temporary forts: plan from the beginning on it being an "upper fort" that supplies things for the "lower fort," heads up the defenses, and actually does trade. You lay it out so that it'll be optimized for that, make sure that every workshop you build up there is really better near the surface, maybe even hold off on metalworking until you get the lower fort going (though, if you don't make it a priority, you won't have a forge set up until two years in, and you won't have decent weapons to combat early invaders), and be careful about how you make the connection (though caverns can destroy the best laid plans).
Of course, whenever I do a volcano embark, I end up just building my fort near the surface, the only thing I usually want from the deeps is candy, and that stuff is so light that it's fine if I have to haul it to the surface.