The inverse of the Absolute Manhattan (or Modified Manhattan) distance, being the 'attraction' level, then?
(And, to be honest, I've never used burrows to keep dwarves safe during invasions, I just use burrows to first of all get anti-invasion defences and tunnels dug first, and then hardly anyone ever has to go beyond the outer 'detection ring', at least at ground level, without me knowing about it so I can send along an escort.)
Can I still suggest that, like each military unit (group) can have a separate go-to (or patrol) point, that a 'mining attraction' point would be most useful if it could be assigned per-miner. In fact, make it an additional element within the Burrows scheme. As well as (arbitrary shaped) areas/volumes being defined, set one bias point/strange attractor per burrow. (Dwarves associated with more than one burrow sum the strange-attractor-modified preference levels from each of the two-or-more burrows with such a point set.) This would be useful for
all job-preferencing burrow uses, from generally getting their snacks and refreshments from a given set of near-prefpoint stockpiles to
whenever they can picking up the raw stones of a particular stockpile, but letting them go further afield when their primary sources cannot
I think integrating into the Burrow interface would be easier, and unless you're making whole-map burrows (or, in effect, summing to that size across the multiple burrows that any single dwarf is assigned to) it would take very little extra cycles to calculate
just the priority/distance factor across a burrow. Even if you're making it path-related.
But this is your idea, not mine, I'm just riffing on the theme.