[joewatch]

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Interesting line. With regards to flop, however, if we check and he pots it, how do you leave AAxx out of the range? I don't think a LAG check behinds with AAxx here because it would be out of character. He's going to represent AAxx here with our without so often that if he checks behind its going to raise eyebrows.

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No, I don't think you can leave AAxx out, but LAG player will often check AAxx top set on the flop as a slow-play. After check-raising the turn, if AAxx is still the nuts and villain reraises, call or fold depending on the implied odds.