A marine band harmonica tuned to D works for me. Blow into first hole for low D or forth hole for high D. My ears do the rest. And I can play along with myself too... Can't do that with a clip on... Robert.

There is a pretty good article on this idea on Wikipedia under Pythagorean tuning with some sound samples..................if you can figure it out let me know....way to much for this boy...whew!  I'll stick with 440...though I have to wonder how some of those medieval tune that Jessica Coumeau plays would sound...as for me and my house Old Joe Clark is about as wild as it gets.   Might just drop her a note and see what she thinks............if anyone would know she would be at the top of my list as her wizardry on a dulcimer is something to behold.  

https://en.wikipedia.org/wiki/Pythagorean_tuning

 Hey Al, question for you: "Have you tried tuning with a tuner set at 432 mhz vice 440?   Checking some video near the link you posted above.........I've used it before and thought it was a bit odd....how about you?

Tuning Tip -- Never try to tune a "silent" string.  Pluck the string and while it's singing turn the tuner knob you that think is the right one 1/4 turn slack (not tight).  If you do not hear the singing string lower in tone, you're turning the wrong knob.  But since you slacked first, you won't snap it accidentally.

A = 440 is merely for calibrating your tuner.  But that A is actually an octave above the middle string A of a dulcimer tuned DAd.

For a standard dulcimer tuned DAd, the bass D should be 146.8, the middle A should be 220, and the melody D should be 293.7.

Ellozz, for a 27" dulcimer the string gauges you are using seem very reasonable to me. Just put on some glasses before you tune and hope for the best.

I think you s/b using C [chromatic] mode with that tuner. V is for violin, G, guitar and B, Bass.

Another thought is that the strings may be old.  Over time, the metal in strings gets work-hardened from tuning, re-tuning, strumming, etc.  Eventually they loose their ability to stretch and they become brittle.  If you are still using the same strings that were on the instrument when you received it, I recommend putting new ones on.

I'v found a lot of MD tab/smn is written an octave higher than it is played. Many new folks miss the fact the melody string(s) tuning [DAdd] is D4, the D one whole step above middle C [C4].

I suspect  ellozz  has a rather long VSL, maybe 30" or more, and probably needs to use .009/.010 on the melody string. If this is true, smaller gauges on the other strings may be in order also.

Ken always knows his stuff and when I started playing years ago got me straightened out on the string tuning notation.  I was breaking strings like you and my problem was related to exactly what he was talking about.  Those J64 should work fine for you but since they are not and you have a tuner there are a couple of things you might want to check.   First, check to see what the calibration on your tuner is set to...........is it 440?  Second, try this tune your base string to where there is just enough tension to get a clear sound.  Not to floppy and not to tight.  Check and see what your note is with your tuner. Tune it to D.............middle string.........tune it to where it is making a clear note, again not to tight and not to loose.............check it and tune it to A...........when you get to the melody strings repeat the process and see what note they are playing.  This is where I was messing up when I started......I was trying to tune way beyond the d, going into an entirely different octave.

On the other hand, as Ken points out your fret board may require entirely different gauge strings because of its length......until you get it worked out I would tune CGc............of course that is your choice..............for me DAA and a noter or DAA and fancy finger hopping as I call it, is the way to go as a beginner and an advanced player. This link might help you.............

http://www.jcrmusic.com/Learning.html

It all depends on what the current string gauges are, and the VSL -- the Vibrating String Length, or distance between the nut and bridge.  Unfortunately "extremely taut" is sort of subjective.  What's extremely taut to you might not be to someone else.

Tell us the VSL, and ask your f-i-l what gauges of string he had on the dulcimer when he gifted it to you. 

Once you know the VSL you can go to the Strothers String Gauge Calculator, enter the VSL and choose "d"  not "D" for the note you wnt to tune to.  The calculator will tell you what gauge the string should be for that note and that VSL.  Be sure to select "d" not "D".  Most people today write DAd rather than DAD, because that tells the reader that the bass string D and the Melody string d are an octave apart -- the melody string being higher in pitch.

Usually a melody string that can tuned to A can also be tuned to d, although it certainly will be more taut at d than at A.

What is your 'scale length'- the length in inches from the bridge to the nut?

And do you happen to know what gauge/thickness of strings are on it now?

Sometimes the tightness can seem extreme to a new player and yet not really be too much.  After all, the melody string(s) are not actually breaking when tuned up to high d, right?