Have Matt and some of the other guys do a few Primary songs in a "Beastie Boys" style–where each guy takes a turn singing one line but all three sing the word that rhymes.
Then you could sing the following:
Priesty Boy 1: Book of Mormon stories that my teacher tells to *ME*
Priesty Boy 2: All about the Lamanites in ancient histo-*RY*
Priesty Boy 3: Long ago there their fathers came from far across the *SEA*
All: Book of Mormon stories that my teacher tells to me.
(Then seamlessly transition to next song using same beat)
Priesty Boy 1: I looked out the window and what did I *SEE*
Priesty Boy 2: Pop corn popping on the apricot *TREE*
Priesty Boy 3: Spring has brought me such a nice su-*PRISE*
All: Pop corn popping right before my eyes.
This type of skit takes literally no practice and can be memorized in minutes.