Fact of the matter is that the situation you describe is a phase of the tourney, when in fact it becomes a crapshoot. It seems that skill will matter less and less, save for one thing only: a good push/fold strategy. (and maybe picking on weak opponents to increase steal success)

Allthough icm considerations start kicking in more and more when deep, I still think that a good push/fold strategy might be one of the few edges left for you in those spots.

So my initial response is to try to

1. steal blinds and antes with hands you are prepared to shove lighter on those stacks, preferrable in late position.

2. Try to double up and tighten up AFTER that succeeds as most others will be obliged to gamble and you are temporarily off the hook. In any case, I do not see any  advantage in getting into hands and than folding vs agression..

You might try to pick on guys specifically whom you have seen folding incorrectly respective to their stacks.

What remains is, that the tools you have at hand as a poker player in those circumstances, are severely limited. So playing toerneys that are less of a crapshoot are of more advantage for skilled players imho. Unless you specialise in perfect push/fold and make THAT your edge next to playing big volumes of these.. As big volume is the only thing that will bend the variance blows into +EV if you have to rely on the push/fold strategy almost exclusively.