You might consider Planetary geared tuning pegs for violin, viola & cello which presumably share the appearance of your original pegs. You would retain the traditional look of the dulcimer but have a more manageable tuning peg.

Haven't used these on a fiddle or a dulcimer yet, but I am considering it for a nice Appalachian dulcimer given to me by Ron Baxter a few years ago. Neil Brook of Preston, Lancashire occasionally uses planetary geared pegs on his hurdy-gurdies where the appearance demands pegs, but also fits standard geared tuners for ease of use where that's the important consideration.

Ross