I would contact MTI (www.mtishows.com) and ask them. I have noticed that they have been a lot more customer oriented lately - I think using recorded music is a long shot but they have developed some recordings for use in rehearsals (maybe just for the kids versions of their shows). They might let you use one of them in a performance. The standard contract prohibits the use of recorded music.

I contacted another royalty house and asked to do a show with music (rather than a musical) and substitute other music. I got permission to do it but they did not reduce the royalties for the show (although there were no music rental charges). We had to pay royalties for the substituted music.

From the actors point of view, recorded music is very different. With live musicians they can and do make a lot of adjustments during the show - pace, timing, covering or helping through problems and so on - they really do "accompany" the singers. With recorded music the music has the lead and the actor has to follow the music. This is particularly a problem with songs that have a long musical intro before singing begins. Live musicians adjust their tempo to make sure they arrive at the right place in the music when the actor needs it. With recorded music it is up to the actor to handle the timing. In one rehearsal using recorded music, the actor got to the vocal point several seconds before the music did. There was a long awkward pause.

Either can work but there is a significant difference.