The related Eastern Orthodox Church, officially called the Orthodox Catholic Church get's along quite fine without a pope - as the Anglican's do.

Why not cut costs and try doing without one for a few years, and see if one is really needed. After all, J Offer seems to often indicate their role is not that locally significant any more anyway (I also note Sinead O'Connor also seems to indicate a pope is not needed anymore).

BTW, an interesting interview of Sinead from 2010:

Sinead O'Connor