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This is actually a push here because he calls with any flush and any 2p/set and you don't want river cards killing your action.

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Actually, against the described opponent, I think it's pretty close between pushing and just calling and letting him push the river.

The one time I played an opponent this crazy, he eventually started folding to my raises (after like the 3rd buyin), but would still likely bet all-in on most rivers *no matter what his cards were*.

He's not *quite* firmly on the hook here yet, so calling might be better than pushing, but I think he's calling a push often enough that it's better, for the reasons you stated.

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I was kind of torn between the two options as well. If you push you are certainly getting value for the hand, but your cards are pretty much face up unless he is retarded. Calling loses value from Ah (or costs you the hand if it hits), but makes it considerably easier to get value against pairs.