Setting up for CGG

This is going to be one of those long, complicated rambling posts which is generally the product of not knowing enough yet. Thank you for your patience.

I got a lovely David Lynch dulcimer a month ago. It hasn't been played for 17 years (or really, ever). The original customer who commissioned the instrument never played it. I quickly discovered as a brand new player that DAD is not my friend (or my fingertips' friend), and I found a nice happy spot at CGG, using my fingers intead of a noter, flat-picking, and throwing in the occasional chord. After removing the second melody string, I like the sound I'm getting.

I am under a strong suspicion, however, that 17 year-old strings are seriously due for a change, even though they haven't been played until recently. For one thing, they can't hold their tuning for 30 minutes of playing without going slightly sharp (or slightly flat, if sitting all night in the case, in an old house, where temperature and humidity changes a lot).

From everything I've read, Dave tuned his instruments to DAD. In this case, he used closed geared guitar tuners (Gotoh), and a 26" VSL. Obviously, when I tune down to CGG, I'm changing one aspect of that set up dramatically. So as I look at replacing strings, I'm wondering if I need to be looking at a different weight of strings (next purchase is a micrometer, to figure out which weights I have), and whether there are considerations about the way they would interact with the tuners. I like the way the current strings sound when they're in tune--but they don't stay that way. I expect some fluctuation, but I kind of think it shouldn't be quite that frequent. Yes/no??

Thoughts, suggestions, and hints in the right direction are all appreciated, with the caveat that I'm looking to stay in CGG (where I'm already happily at home), and I'd like to get things working well in my current tuning.

(This is a wonderful dulcimer, and it is amazing to play!!)