This issue has come to a head for our next funeral singing engagement, where the hymn chosen by the family each have at least 2 tunes, and in one case, a mighty 7.
That's why we include pre-funeral music checks in every funeral singer fee. This means we sort out all the logistics of the music - which tune, which key, which version, number of verses, etc - in advance with the organist or minister (or both).
If no organist is available, we ensure our professionally recorded accompaniments match the above requirements. We also rehearse in advance of every funeral, both privately and with any organist beforehand, to ensure the best musical farewell.