Yelp, a swarm is indeed a pretty sight...kind of a Catch-22 when it's from your own hive, though. :) I'm very familiar with that scenario. :-\
I would not block the entrance. You've got it opened to roughly a 4" opening? I don't even know if I would reduce it that much. Sounds like you have things pretty well taken care of...time will tell. This is my first year and had multiple swarms that I had to deal with. One swarm swarmed twice...the second time it stayed put. Time will tell, especially the next day or two. In my opinion, it's up to the bees now. ;)
ETA: How are you feeding them? Baggies, jars, top-feeder, boardman,...??? I don't know how your honey flow is but it's basically a time of dearth down here with very little sources of nectar....beware of robbing...if robbing starts you may indeed need to close it up for a while or if nothing else reduce the entrance down to the smallest notch.
Best wishes,
Ed