This is very interesting, and it shows why the Strait is urgently in need of a back up. I don't know what that would be or what would be feasible, but I've seen a lot of people talk about an underground pipe.
There is a great bit of coverage on this by "what's going on with shipping" here: https://youtu.be/r0EvQgLcjMw?t=172
It does not look like this data is part of the paper above.
The choices are then to find a way to get the Houthis to chill out, or use enough military force to cut off the Iranian support for the houthis, or use military force to be confident you have destroyed the houthis' ship attacking capability.