It should not take a rocket scientist to design a Tunnel Boring Machine (TBM) that could be quickly deployed to a mine from a central location.
The TBM would be designed to drill about a 36" hole through collapsed sections, deploying steel pipe in short sections as it proceeds.
A conveyor would deliver the debris from the new tunnel back to open area where it would then be handled normally to outside mine.
As it would be working in soft, loose material, it should be able to work very quickly, perhaps as much as 50-100' per hour.
Such a TBM, due to it's small width, would be easily transportable, one could be required to be available within, say, 6 hours at most from any underground mine.
If anyone with mining or engineering expertise can find a problem with this solution I'd like to hear it.