IMO the easiest way to open the straight is for the US to back down. "The EU helping the US" doesn't sound like a great way to achieve that.
I don't want the EU to join a protracted Iran war.
I don't want the EU to join a protracted Iran war.
Europe cannot contribute relevant naval power to reeopen the strait. They cannot significantly turn the tides in a ground invasion, nor do they have the impetus to. The only thing they can do is legitimize Israel's war, and why would they do that? It's not like America or Israel are any closer to achieving their key objectives, Europe wouldn't even get a tour-de-force out of it. This is purely CENTCOM's fuckup, NATO has nothing to do with it.