I'll take 1 out of 2.

Shill, you say we have to put a raise in somewhere, so when you say it only costs us 1 bet to see what we have on the river, that's not entirely true. Yes, only 1 bet has gone in before you see the card, but when it misses, you're going to raise anyway. That means you're putting three bets in regardless. So try to win the 15 bets on the turn when you may redraw against AA. In fact, if a 9 or 4 came on the river, there's a chance a "smart" BB would check anyway eliminating your guaranteed raise (of course I think that his check would be bad, but there's a chance it will happen).

Forgetting all of this ... who folds in micro-limit to a 21:1 showdown? I might even the BB could mis-click that 3-bet reraise 4.54% of the time!