Paul you are right - the relief (or lack of it) on the fretboard will effect the action, feel and over all playability of a dulcimer. I do somewhere around 200 to 300 resonator guitar set-ups per year - fret leveling, setting relief, cutting nuts and cutting new bridges. And, to get it right, the sequence is relief first, then nut and then bridge. With a dulcimer the player can do nothing about the instrument's relief, unless you want to take off all the frets and sand and re-finish the fretboard !!!! The best playing dulcimers I get through my shop are those with just a touch of relief in the fretboard. I get to compare a lot of instruments side by side so feel pretty justified in saying that a little relief makes a big difference. You can run a lower action at the 7th and still have a beautifully clean playing instrument for chord melody style if there is a touch of relief in the fretboard.
BUT NOTER DRONE IS DIFFERENT FOR ME - Having a touch of relief remains the same - I want that on all my dulcimers. However, I run a much higher action at both nut and bridge. I want absolute clarityfrom my melody string, working off an in-strum lead and using very stiff picks (quills of wood strummer). I've just measured my own noter drone specific instruments - the ones where I have cut new nuts and bridges to set the action to suit my playing style - and my prefered action is way, way higher than nickle and dime. For example the Prichard replica I have, which I cut a new nut and bridge for, has an action of 1.5mm 'above' the first fret (I could sit a dime on top of the fret) and 3mm above the 7th. I'm using 0.013 gauge piano wire for the melody string on that instrument. I have an old dulcimer with the action even higher but the fret pattern is visibly shifted to the left on that dulcimer and the first fret even more so. With a fret pattern set by ear on older dulcimers you often see this shifted 1st fret - and it is due to the nut height that the early players would use. I see that Bobby Ratliff at Slate Creek Dulcimers, who builds noter drone specific instruments, fits a floating bridge so players can intonate the melody string if they change action height or string gauges or tuning tension. It is a very good idea as I certainly need my VSL slightly longer than the VSL of the fret scale. Kevin Messenger builds this fret pattern shift into his Prichard replicas. Because pretty much all contemporary dulcimers are designed around D,A,d and chord melody playing the bigger volume builders standardise their action, string gauges and pitch intonation around set parameters. This is why if you tune the open strings of many contemporary dulcimers to exactly D,A,A and play with a noter the darn instrument plays sharp 
So us noter drone players end up tuning the drones against the fretted root note on the melody string (the 'd' at the 3rd fret) and accept that our melody string open A will be slightly flatter than our drone string open A
So, coming back to string height, no one set height will suit every dulcimer or player. However, you can't just change the string height or gauges or tunings and expect all to be perfect. And, if you do get a comission for a build from a noter drone player have a think about the implication on the fret pattern that running a higher action and higher string gauge will have. And don't forget that a noter drone player doesn't need equal temperament fretting as they are not playing across the strings fret against fret - you could opt for a mean tone or just intonation or quarter-comma meantone or simply set the frets by ear 
