I appreciate that I am much less knowledgeable than you and others here to comment but I have been following the debate with interest and here are my thoughts for what they are worth.
In this situation you will be left with 5927 chips if you fold. You will have 12979 if you call and win. So with true pot odds for chips EV you need to have 5927/12979 = 45.7% chance or better to make it a profitable call. If this was near the beginning of the tourney and you had your starting stack this assessment would be appropriate. Perhaps you feel you had an edge on the tourney and you may therefore want 50% chance to call.
However IMO whilst you are nowhere near the final table or the prize money you have increased your stack fourfold and there must be some significant ICM effect. So +EV chips does not equal +EV prize money. Doubling your chips does not mean doubling your expected prize money. . At a guess 5927 chips might equate to expected prize money of about $9. 12,979 chips would of course not give proportionally more expected prize money- 12979/5927*9 = $19.70. I would guess it would be about 16$. So if you fold you would expect to win 9$, if you call and win you would expect to win 16$. You now need at least 9/16 = 56.25%. Add on a small edge and to be +EV prize money you may want 60% chance of winning not 50% as per chips EV.
Using Pokerstove you get only 70% against a random hand, and you will only get required 60% against his range if he is pushing with 50% of his range which is 33+,A2+ K2+,Q2s+,J4s+,T6s+,96s+. I think he might be pushing light here in the BB with only 1 oppo. left, but no evidence to suggest this light. Its a fold for me.
I appreciate that the numbers in para. 3 are estimated but I think give a reasonable assessment of calling requirements. The ICM programmes I have seen only give single table situations and shoving range rather than reshoving ranges. If anybody has access to programmes that calculate above I"d be happy to be corrected.