Well let's steal an idea from the pirates.
Many pirate crews were quite formalized, drawing up detailed contracts concerning different crew members shares and duties, as well as common rules agreed to by all. the Captain in many cases was the individual who the crew decided to be the captain, and once the voyage was over he was no longer a captain, although he frequently would keep the ship itself as part of the loot for a second voyage, if it was not sold to get more gold with which to buy rum. Point is, pirates were capable of a great degree of formality and legalism, although any appointment as captain or quartermaster or mate or whatever was a temporary posting which only lasted as long as the current voyage. I say our "ministers" be any pastafarian who is voted minister for purposes of ceremony, as per the pastafarians involved. Basically, any pastafarian can perform a marriage, so long as the other pastafarians at the ceremony agree that he/she can. Of course a marriage being a formal, if not solemn event, any pastafarian worth his noodle will attend in full pirate regalia.
As an afterthought, maybe our minister is simply the pastafarian present with the largest pirate hat? which raises another question: do we go by height, width, or weight?