I remember reading in The TImes that the announcement of Avenue Q moving to New World was a deal that was completed in the zero hour. That the producers found out about it just before the closing night performance of the show on Broadway and thus announced it from the stage after the show.
Also, there might be some time between them announcing a move back to Off Broadway with In The Heights and it closing on Broadway. If I recall correctly, another show that also did the same thing, 39 Steps, was one show that didn't announce the move the second it closed up shop on Broadway.
And, I don't think that In The Heights moved because that was the only way to keep it open. Regardless of the size of the show running costs are always cheaper off Broadway. And, I think that the fact that it was selling very well at a space that was very hard to get to had more to do with it moving rather then it having to move to stay afloat.
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll