65 pushes are also not as good here. If they pass, then it doesn't matter what cards they held, if they call, you are a dog against almost any hand (incl those I mentioned above) and with weaker players again you could even be dominated by A6s or A5s.
I don't think a 65 push is a particularly good play either in this position, but at least you know what you are doing - semi-bluffing. Obviously you are a dog to anything that calls, but usually not a big dog and undeniably a lot of hands that should call will fold, quite often a5/a6, I'm pretty certain 85 folds.
If an A7 push does get called by a weaker hand, your edge is unlikely to be very large, with big cards being near to a coin flip and weaker aces sucking out or splitting the pot a fair amount.
I really do agree with your commments about the luck element in turbos, but don't think that the answer is to gamble when any opportunity presents itself.