I prefer calling this preflop and squeezing KQ off.

AP Bet again, we want value from worse Qx, PP and FD. OTR I probably x/c v a reg and shove v a fish

I like your choice of hand to squeeze. It's an UTG open so I want a better quality hand which plays well multiway and OOP. AJo and KQo can be very tricky against a strong range and multiway OOP.

Flop is a standard c bet for value.

The turn I suspect is close between a bet and a check call. Depends on how wide you expect him to call his second pair type hands. You didn't say which was the whale and which the reg, or did you means an answer for both?

Versus a whale I'm probably betting the turn and going with it on the river.

Versus a reg I'm probably check calling and folding the river because I doubt he'll jam QJs, and he might not even have QTs in his range.