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I'm not sure laying down AQs preflop here is good play.

The most likely range of hands that villain has (given the table and his preflop actions) is AA-JJ and AK, all to which I am behind on the flop. AQ-AT is not entirely unlikely either and they are also pretty bad for me. Ok, the flop wasn't swell, but villain's bet laid me 4 to 1 to call to chase the gutshot straight.

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First, you say that you are not sure laying down AQs there is a good idea, then you post what you think his range is, most of which have you dominated. On the flop, you are not ahead to a single one of his hands (JJ hits a set, QQ-AA have an overpair to the flop and have you drawing dead, AK has you drawing dead to 3 outs (the other kings). Add TT to his range, and you are behind yet another hand.

So let's say you have 3 outs at most, maybe even 2 or 1 possibly, you would need about 8 to 1 to call there. Even with 4 outs, you need about 6 to 1. You are not getting near the odds you need on the flop, which is a flop you should have never seen with your hand in the first place if you trust your reads a single bit.