Henry Miller's Theatre is being leased by Roundabout for shows which they hope will play an extended engagement, instead of the situation with Studio 54 and American Airlines where another show has to come in to satisfy their subscription audiences. However, if one of their shows at Henry Miller's only plays through its limited engagement and they have nothing else lined up to replace it, the theatre will be made available for limited engagements of commercial productions. If Birdie doesn't run past January 3, you may see a limited run of a commercial play not affiliated with Roundabout at Henry Miller's this spring. (There's a LOT of stuff on the way for the spring, not all of which has been announced yet). I wouldn't expect any commercial musicals to book Henry Miller's, knowing they can't stay there indefinitely, but a 12, 16 or 20 week limited engagement of a play very well could.
As far as other available theatres for the spring, isn't the Belasco expected to be back in play by that time, following renovation?
Begin at the beginning and go on till you come to the end: then stop.