The two succeed Fra Fee and Amy Lennox, who depart the show October 1.
The viral musical was set to perform at Royal Albert Hall September 20.
The winner will get to hang out with Lin-Manuel Miranda at the musical's opening night in Germany.
The new musical will play The Factory Playhouse in Hitchin, Hertfordshire.
The new dark comedy from the makers of The Play That Goes Wrong will premiere this fall.
The tribute to the late composer and lyricist was part of the Barcelona Grec Festival 2022.
The two succeed Fra Fee and Amy Lennox, who depart the show October 1.
The viral musical was set to perform at Royal Albert Hall September 20.