Bill Snibson said: "With AF closing in January that is a very fast turn around for any show to secure that theatre, figure out the technical aspects, go into rehearsal and be ready to open before the Tony cut-off, right? It would need to be a small play or very small musical."
This literally happens every year. Shows close within the first half of January, they have 3+ months to load out, load in, tech, and start previews in advance of an April opening, or even a March opening. It doesn’t need to be a turnaround as quick as Potus or Lady Day or the 2015 Spring Awakening.
Remember also that shows are long in the works, with theaters all but promised to them. The tech specs of the Jacobs vs Belasco vs Longacre are not significantly different when you’re dealing with plays or modestly-sized musicals.