I basically believe you're right, but I can't wrap my head around this: How is it that they still have any control at all of the strait after all of this? Is their significantly depleted missile force enough of a threat as long as they have any credible capability whatsoever left?

Iran "controls" the strait by shooting missiles at any ship that passes through without paying them a protection fee. This includes ships that pass through Omani waters, which it has no legal control of. It's terrorism, and also an act of war.

Iran built thousands of fast-attack speedboats which patrol the strait, get up close, fire a few missiles, and quickly return. This video gives a good explanation of their strategy. https://www.youtube.com/watch?v=GKJHaODzP-0

This can be mitigated by the US/Gulf Countries, with a large number of airplanes / drones patrolling the Iranian shore, and preventing these boats from launching.

The straight is narrow enough that they could use artillery to hit the ships in it.

And for US and/or Israel to prevent it, they would have to occupy the correspondingly wide strip of Iranian coast. At which point we're talking about a massive ground invasion (and of course then the same artillery would be firing at those troops, so you can't really just stop there either).