The multi-div idea should still help, but different than I first recommended...  instead of doing a 4-div then a 2-div, what we need is a 4-div without inflate_by_longest_edge and then a 4-div with inflate_by_longest_edge.

It occured to me that we don't really need to jump up to the next div size, we just need to include the inflate for the second pass - that way we're still only checking a small number of polys in the second pass, but we make it big enough to account for the region-spanning issue.  I just used 4-div as an example (it's reasonable), but I'd leave that as a user-defined thing... it might need to be 3 or 2, or conversely 5 or higher might even work (the higher, the faster).  Just use the same value for both pases, but don't add the inflate until the second pass.

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