Oh, that sounds very hard for your friend. If this idea of 'stepping down' is just coming from the vicar and he is pressuring your friend to make the decision, maybe a wider discussion with more of the church community is needed, if your friend is unsure what to do. From what you have said, his work is valued and the church would miss him.
The worry that he is cohabiting with his girl friend will be solved when he is married, it is not like he is not committed (from what you have said) and I guess it could be just too complicated to bring the wedding forward.
Does the vicar expect him to alternatively move out of his home until after the wedding? Without knowing their circumstances it is difficult to comment on whether this would be possible and it would seem like doing this would just be for 'show', if he is equally committed now as he will be after the official marriage.
Personally, I think this type of problem has been exasperated by complicating the process of getting married. If you look at the history (see below) for centuries getting married used to be a much simpler affair.
"With few local exceptions, until 1545, Christian marriages in Europe were by mutual consent, declaration of intention to marry and upon the subsequent physical union of the parties.[288][289] The couple would promise verbally to each other that they would be married to each other; the presence of a priest or witnesses was not required.[290] This promise was known as the "verbum." If freely given and made in the present tense (e.g., "I marry you"), it was unquestionably binding;[288] if made in the future tense ("I will marry you"), it would constitute a betrothal."
( en.m.wikipedia.org/wiki/Marriage )
Whilst I see there is a need for balance, in that marriage should be thoroughly thought through, the societal pressure to get married in particular way which requires lots of organisation, does, I think, mean lots more committed couples will want to cohabit.
Then again, if marriage is seen as sacramental (not all Christian churches do consider it such, see above link) this escalates the importance of being married before living together. However marriage has not always been regarded as a Sacrament and is still not be all Christian churches, the page I linked to says,
"and many Anglicans consider marriage termed holy matrimony to be an expression of divine grace, termed a sacrament or mystery."
Many suggests some Anglicans don't consider marriage to be a sacrament.
So, if your friend is at all unsure, as to what to do, I think a wider discussion with the church community is necessary.