Flopcheck is the most standard thing ever, if he has a hand he's going to c-bet himself so you're point about not extracting is void. Shoveturn if he's fairly passive, if he's aggrocallturn. That simple.
This fo sho.
His flopcheck and turnraise SCREAMS he has a 9. He's an idiot for not betting most 9x on the flop anyways. But yeah, it comes back down to tendencies. Either shove now or c/r or shoveriver.