I gave myself a 30 second time limit and came up with betting enough to cover his 2 bet win (double or split), but not enough to give up a full swing of 1 bet each. This gives a range of 125-375. I then chose the high end of this range, since it gives you the chance to cover his possible 3 bet win by doubling. So my bet is 375.
Then I gave myself the luxury of unlimited analysis, but haven't managed to come with anything that I think is better. There is no reason to bet less than 125. Covering his double is the first priority. Betting more than 375 still can't cover his 3 bet win without doubling. It does allow for the possibility of covering his 3 bet win with with a blackjack, but at the cost of exposing a full 1 bet swing. I'm not sure whether it's worth it or not. My gut says no.
So 375 is my bet and I'm sticking with it.
I don't think the count is a factor here. It doesn't change the odds of winning/losing your hand significantly. It does increase the odds of a blackjack or a successful double, but we already have these covered.