Found it. Any version of OS X, 10.6.8 or later (including Lion) must be allowing DOSBox to poll hardware it couldn't see before. If I unplug all of the extra USB or FireWire devices from my Mac, DOSBox snaps open instantly. Plug them back in, and it stalls as if it's trying to get info on a device.
So no real problem, I just have to wait a bit for DOSBox to open after it gets done polling hardware. It's likely stalling on a scanner that's turned off, but I haven't bothered to narrow it down now that I know what the general issue is.