Again an interesting thread presumably dug out by spamming bots whose "contributions" were swiftly deleted.

The pairing but-and-ben is old Germanic heritage, always meaning "outside and inside". In the context of the song, I would understand "drink a health to him publicly, not only in private". Accordingly, the disguise is very thin, quite on purpose.

A moorhen was and is indeed a species, not only the female sex. In traditional English, any bird can be referred to as "she", even if clearly biologically male such as a songbird actually singing.