Just thinking here...see if this makes sense:

For point #1, I think he'd fold air and hang in there with a weak ace, or a seven. He'll probably reraise with that magical 4. This may be a case of "only bet/raise if you WANT to be called." Which is to say, you're hoping he'll call with air,or a seven, or a draw.

If you want to see the showdown, you can either pay 2BB by calling down, or by your method (which is not safe).

You can make him pay for betting a flush draw by raising the heads-up flop, since a flush draw by itself only has 35% equity.