It's quite a telling post imo. 

I don't really like the way you describe ICM here as more of a philosophy "all of the money is in the top 3". There is money in each payout spot.... this is what an ICM calculator is for.  If you use both the philosophy AND the calculator, you are double adjusting.  The HR nash calc can definitely set up this hh, not sure if you are having problems with the software, or just the general strategy we should use.

I often hear this question from players who aren't stealing enough. We don't wanna just open super wide, but we should be opening wide enough that we feel we can snap call here. So often the answer is not about how to play our nut hands differently but what we are doing with the min/fold aspect of our strategy.

This hand to me is about the shorty in the BB.  If chipleader is competent, then I suspect they (like I do) feel like you have a (super) tight min raise fold range in this spot. This is going to tighten up their 3bet shove range (whether its true you are tight or not).

Its true a competent villain will try to put pressure on you here but I'm not convinced they are even shoving much wider than KQo here.  They are prob slightly wider but given everything JJ will prob play better as a shove here (we should compare shove vs min call in nash calc both the specific hand and overall strategies).  If we want to induce here we want it to be only if villains' will reshove quite wide giving us more dominated flips.

You've also capped your range vs what you described as a competent villain, so when you shove here, you aren't so likely to have JJ+, and villains (especially chip leader) are going to call you a lot lighter.  This all might not be of much concern, but at the very least we should be aware of what we've done.

Mostly the only reason I say this is because its tough to rep a lot of min raise folds if the bb is so short.  Even tho we are ahead of KQo, its prob not our favorite hand to see if its the bottom of villains range.

Shove pre or open up your min fold range (prob both)

edit: also with the shorty about to hit the blinds this isn't the time to bust our stack with a flip I should think.

Min call it its high variance play imo, its better to open shove there all ur opening range vs regs.

Vs fishes ill have min/call min/fold range