Those are great looking pegs! Can you get the gauge of the remaining string? There's a possibility all 3 strings would have been from the same wire (the peg grooves may give a clue) so unison or 1-5-5 pitched up a bit from D are possibilities. The scale length and string gauge should give us a clue. It will be interesting to know if the string is looped by hand or an obvious commercial banjo string. That may help date the last re-string.
The peg closest to the fretboard is just a little out of round and so is the hole. It could easily be fixed with a reamer and shaver, which I have.
Those are great looking pegs! Can you get the gauge of the remaining string? There's a possibility all 3 strings would have been from the same wire (the peg grooves may give a clue) so unison or 1-5-5 pitched up a bit from D are possibilities. The scale length and string gauge should give us a clue. It will be interesting to know if the string is looped by hand or an obvious commercial banjo string. That may help date the last re-string.