Yes JI is Just Intonation -- a system for laying out frets which is different than the Mean Tone system used for modern instruments.
JI has nothing to do with having, or not having, a 6+ fret. Until now (I'm building a dulcimer with JI fret spacing) I've never had or played a JI instrument. But I've also never built or played instruments with 6+frets (well, just a few).
On dulcimers with JI fret layouts, notes are just a bit 'sweeter' to the ears, than the same notes on the same frets of a Mean Tone dulcimer. Mean Tone is more or less world-wide, and allows instrument from many different places/builders/cultures to play together more easily. In a group of instruments where most are Mean Tone, a JI instrument will sound "off" when playing a scale alongside a Mean Tone.
At this point in your dulcimer journey, I honestly don't think you should even think about JI vs Mean Tone, except in this respect -- IF that Warren May instrument is one of his older (pre-80s), JI layout dulcimers, understand that it should probably be used for solo play rather than ensemble play. Not all Warren May dulcimers are JI. Not all have a 6+ fret.
You also asked about string gauges for a 20" VSL: "If I was in DAA i would have 18 & 18 for the AA's? Is 12's too way off, since that is what Warren said he would used, or could he have forgotten it's a small size - is there a size good for both or either tunings DAA & DAd?"
Yes, with that short of VSL, 12 gauge strings would be too light for the A. Warren may not have remembered the VSL correctly. Strings that work well for A also, generally work with d as well. Or you might experiment with 18 and 16 for the mid and melody strings.
updated by @ken-hulme: 01/08/16 08:52:16PM