Great info from Ken.
I do want to add though- you said this dulcimer has no 6.5 fret. That would make it a little hard to play in DAd using chord style playing. You'd frequently get frustrated not having that note on the melody string.
However, if you try a 1-5-5 tuning (DAA or CGG) you would have most needed notes on the melody string. You can try out playing mostly on the melody string and leaving the other strings unfretted, sounding as drones. That's a very pretty older way of playing and this dulcimer might be perfect for giving it a try. The 'home' or tonic note of the tune is then located at the 3rd fret of the melody string.
For DAA/CGG tuning, you could use .010 or .012 gauge for the melody AND middle strings, and then as Ken suggested a .020 or a .022 for the bass low string. The thicker the string, the tighter it will be, so you don't want to go too tight/heavy on an instrument with wooden tuning pegs.
If you are used to fretting with your fingers, you can try 'finger dancing' style, where you fret the melody all on the melody string and play the other strings open and unfretted. It's a pretty way to play! You get the ancient sound of the drones.
Does your wonderful Sunhearth have the typical sunburst sound holes? We'd love to see a picture of it, it must be beautiful!
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updated by @strumelia: 12/12/21 08:07:26AM