Strategically, it seems like a dumb move. Right now, Congress is unlikely to approve Trump’s request for $200B to fund the war effort. But if Americans can be convinced that Iran could somehow hit American cities, they would call their members of Congress in a heartbeat and that money would presumably flow without interruption.

Why time the medium range missiles now? It seems like yet another own-goal for this desperate and poorly coordinated regime.

I can't speak for Iran, but it may be a warning against attempting to land troops on Kharg Island. They're showing that they've been "nice" so far, but they have escalation paths America may not have considered. I think most people thought they were limited to short range missile strikes.

Or the US could just stop bombing Iran? Then there would be no reason for Iran to attack American cities.

Americans can be convinced of anything without too much effort so that isn’t really a factor here.