A common cause of the rpms hanging up is out of synch carbs. You said you "had the carbs synched", did you do it, or did somebody else? It seems like more often than not, when you pay somebody else to do carb work on these bikes, it doesn't get done all that well.
Another issue could be one or more leaks in the rubber insulators between the carbs and the cylinder head. You can try spraying some carb cleaner all around them with the engine running. If the rpms change from doing this, then you have a leak.
It could also be as simple as needing to adjust the idle stop screw. I don't remember exactly where it is on the 350F, but you'll see it somewhere on the carb rack. It's the single, big, knurled edge thumb screw. Turn in to increase idle, turn out to lower.
You're correct in that the choke on your bike is not an enrichening circuit like on newer bikes. It simply closes a plate in each carb to increase the vacuum on the jets and pulls in more fuel for a given volume of air. Yours is also one of the earlier style chokes that does not have an idle speed cam on the choke arm, so closing the choke has no physical effect on the idle setting. When the engine is cold, you either have to hold the throttle open with your hand on the grip, or turn in the idle stop screw, and then turn it back down when the engine is warm.
