RESULTS
Thanks for all the responses. It sure is tough to play top pair-bad kicker out of position, so I'm still not positive what to do with the hand. I think the line I chose, while passive, at least avoided building a big pot in an unclear situation.
I folded on the turn. The river was a 10 and it was checked around. The original preflop raiser showed KTs; the button and SB both showed AK (!) for Broadway and split the pot. I bet nobody scoring at home had them on those hands; but it turns out I actually was a huge favorite on the flop!
The dilemma of flop play is that there are so many possible draws out there, and if you want to bet enough to drive all those draws out, then you're going to lose a ton when it turns out you are already behind. I don't know if there's a good answer.
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