Hmm. Pretty tricky problem. What's an out of the box way to counter this?

Got me. The obvious answer is an Iraq-style ground invasion, but no one wants that (and that's kind of in the box). The other obvious answer is "time machine" and undo the initial decision to start this war with no answer to the Hormuz problem - but that's too outside the box.

I suppose you could have a "limited" ground invasion just to seize the coastal regions and islands in the area surrounding the strait itself. No easy feat, given that Qeshm is a little more than half the size of Rhode Island and you'd have to control a hundred miles of coastline at least a few miles inland. That would probably be very foolhardy, but it's a half-measure short of actual regime change.

I do not include the proposal you linked a little upthread, because that was a silly and uninformed impossibility by someone who might understand game theory but not much else.