If you can get an immigrant miner to survive for a few minutes, you can tunnel down into one of the caverns and gather plants for food and to start a farm.
The good news is that if you can get a miner in a "second" fortress and seal the exit, he can work on a raising drawbridge airlock so the temp fort is more than secure.
Personally I'd avoid the caverns. You've had how many forgotten beasts so far? Really want to open another cavern and risk more? Most places have soil or clay layers that are more than 1 Z deep, so you should be able to get a farm going near the surface, if you can get some seeds. You might have to dig a tunnel to your old food / booze stockpile and make a few raids (with a door and bridge in place to seal the entrance up. Maybe just a door and then wall it up afterwards.)
Or if you're feeling cheap, autodump in dfhack. Maybe just autodump some food and booze for 1 greedy miner immigrant, and make everyone else raid the stockpile until they have seeds.
But I would probably build my temp fort in tiers of security. The tunnel to your old fortress and the main entrance are tier 1. If tier 1 is breached, they are stopped by the defenses at tier 2, etc. Just so that if a butterfly jams a door and bridge doesn't go up in time, you haven't lost all.