I play unwound bass strings. I find they help me get the 'high silvery' old time sound I prefer, rather than the more mellow modern sound. Most of my dulcimers have a 27" VSL and I find that a .018 plain steel string works pretty good for the range of tunings that I use. I you like that mellow 'guitar-like' sound then use a wound bass string, IMHO.
D2-D3-A3-A4 equidistant -- Sure. Why not. I've not seen/heard anyone do it, but don't let that stop you if you're looking for baritone/bass sound. You'll probably want a new nut and bridge set up for 4 strings rather than filing a bunch of notches on the ones you'll have.
re - vibration on the back side of the fret. I'd say that you're not fretting quite hard enough. It could be the low tuning with the strings you have, but it sounds more like not fretting firmly enough. The sort of 'standard' action height is what we call "nickel & dime". That is strings just touching a dime placed next to the first fret, and also just touching a nickel set on top of the 7th fret. You can lower the action more if it suits you, by sanding tiny amounts off of the bottom of the net and bridge.
The string gauge calculator many of us use is at http://www.strothers.com/string_choice.htm It is noticeably light , however, and you can generally go 1-2 gauges heavier.