Wooden Tuning Pegs - Grrrrrrr

I've played guitar and changed strings successfully for well over 50 years.  I've finally met my match in dulcimer wood tuning pegs.  I removed the two year old strings from my 1969 handmade dulcimer, treated the slipping pegs with "Hiderpaste", reinstalled them, twisted them several times, then tried restringing.  Bass string kept slipping, then it snapped.  Middle string did the same.  Melody string somehow was installed successfully.  I don't see that the peg paste had any effect other than allowing the pegs to turn more easily.  They slip just as much (if not more!).  I'm thinking of converting to geared or Grover friction pegs, but I know that may involve hole reaming, which is beyond my skill level.  Any suggestions? (I'm going to go play my classical guitar now, which is reliably tuned up, while I await any replies :))