Raise more preflop, say to around $0.12-0.14.

You have two choices. Either you're deciding that you're okay with stacking off, or you fold right here. If you decide to stack off, you can either call and get it in on a later street, or 3-bet with the intent of stacking off here.

Calling has some significant disadvantages like giving Villain a chance at a free card play and letting scare cards come can will kill our action against hands we beat.

We're usually ahead of his stacking-off range (a little bit of fuzziness here since we don't have solid reads or a larger sample for stats), so it would seem like it's time to get it in. I'd 3-bet to some amount that would give him incorrect implied odds to call with 12 outs, whatever that amount happens to be.