Glad we could be of help and that you got your issue sorted out so well!
Ken is right. It sounds to me like the third fret is the bad guy. As instruments age, frets can become uneven because of wear or the finger board drying out.
There are techniques for leveling and re-rounding frets. If you don't feel comfortable working on instruments, a guitar repair person should be able to fix the problem for you.
It's probably not the 2nd fret that's the problem. Check the action height on the 3rd and 4th frets as well. I suspect the 3rd or 4th fret has risen for some reason -- humidity usually. Has the instrument had this buzz even when it was 5 strings?
Contacting Mike is probably your best bet for speedy resolution, unless you have another pet luthier in your back yard!
Your terminology is a bit confusing -- dulcimers have a melody string and two drones - the middle drone and the bass drone. So you've reduced the original 5 strings to equally spaced melody, middle drone and bass drone, correct?
Mike Clemmer Mtn Dulcimer - built in 2002; vsl 28 1/2"; tuned DAdd; strings - .012/.012/.014/.022w; original owner
Basically I'm a neophyte & started taking lessons & studying the dulcimer the last 4 months so an expert I'm not. I changed out the old strings with those listed above & I've tried both larger & smaller middle & base strings but I still have a disturbing buzz on both of those strings when playing on the 2nd fret. Open or any other fret is no problem. The height of both strings at the 1st fret is slightly more than the thickness of a dime & slightly more than a nickel at the 7th. This was a 5 string dulcimer but I've taken off the drone string, moved the base to the drone location & the middle string to the center on the nut & bridge. Space between the melody to middle string and base to middle string is the same. I've not altered the nut, bridge or any of the frets.
Any suggestions are appreciated.