Ok. I had the same slipping problem the first time I messed with wood pegs. What I found to work best for me is to push the peg further into the hole as I finished, maybe going a little bit past where I wanted to be.
Have you used wood pegs before? Just curious.
It's probably going to be 1/8" from the sides to the outside strings, another 1/8" between doubled melody and bass strings and single middle string. The bass set is probably a bass and its octave with doubled melody strings. My 5 string Blue Lion is 5 equidistant strings, 1/8" sides to outside strings.
Look really close at where the strings connect to the pins also
I just thought if the tv tray worked it could also be turned into a table/music stand by adding the top [if needed] and a slanted vertical music /tablet holder.
A tv tray may work. There are some with L shaped legs that are height adjustable. A short board would add extra length if needed.
That's what I use, cell app. I made the recommendation as a starting point. At this time in his journey, if it's screwed up, send it back. I also suspect the op doesn't have a good ear' right now. 
@Tull66, Different strokes for different folks.
My first experience in my dulcimer world was to build a kit. No musical or wood working background or mentoring at all. It turned out good, I still have it. I went on to build some from scratch and to buy some, although none were [are] foreign made. Be aware there are poorly made MD's floating around in the US that are wallhangers also, but they are mostly homemade I think. I have a friend who bought a foreign made MD, It sounded ok to me, but he is very experienced and has made some stringed instruments. Actually, I've really never heard a bad sounding MD in 20+ years, cardboard or home built, lucky I suppose. If you decide to get an inexpensive or questionable sourced MD, be sure of the return policy and get an electronic tuner. Use the tuner to verify that the frets are properly placed. Folks here will help with that. A used name brand is an option also.
Bottom line, you started at the right place, here. You're getting getting input from several different viewpoints, from folks with different backgrounds and experience, all of which have merit.
One other thing, the doubled melody string produces a different sound/tone than a single melody string.
A couple of other points I forgot, a chromatic will probably be a bit more expensive to buy and much harder to sell.
I think many of the reasons will be be focus on tradition and your music interests which will include style of play [N/D or chording] and need for the extra frets.
It will boil down to what you want plus a bit of DAD [dulcimer acquisition disease]. 
I am NOT a traditionalist but I find I play mostly traditional [diatonic] music most of the time when I play with others even though my main MDs are chromatic. I use the chromatic side mostly when playing by myself.
I forgot to add, there are 'chromatic tunings' such as DAA#d, but they are 4 equi-distant strings. These are done on the standard diatonic MD.
There are some things to think about for fret installation;
1. tools; fret saw with depth control, square, hammer/press, measuring device and file[s] for leveling and finishing the ends.
2. where to put the slot
3. the correct size of fret wire
The 6+ is far enough from the nut-0 fret to be rather difficult to place, the 1+ is easy.
It's probably more efficient to pay for a single installation unless you think you may do more of them.
@jost :
Keep in mind that as long as you are playing the melody on one string [the melody string for instance, the other 2 are drones], the tune can be played in any mode [tuning]. Off the top of my mind, DAC [Aolean], CGC [Mixolydian], GCC [Ionian]. This is because a key scale consists of all 7 modes, each mode beginning with one of the notes in the scale. For instance, there is an Aolean mode in each key scale, it starts with the 6th note of the scale as the lowest, or beginning note. The notes are different for each scale, since the "parent key scales" are different.
G key scale = GABCDEF#G [Ionian], EF#GABCDE [Aolean]
D key scale = DEF#GABC#D [Ionian], BC#DEF#GAB [Aolean]
Just for giggles, playing on just one string, no drones, is not a mode or is all modes, take your pick.
I also found this table somewhere in my research. Pretty much the same but there are some differences between this and my earlier chart.
You will probably need a chromatic or use temporary frets [paper clips about .040 or tooth picks may work], tmp frets 0+, 4+, no capo [DAd. Can capo at 3 [DAd] by adding a temp fret at 7+ also.
I wouldn't worry about 'audio quality' right now [you already know what it sounds like], you're just trying to archive the tune.
If you have, and can mostly use, either program you can try entering the note name and matching that with the approximate count of the length of the note played. Just enter the notes/matching count length and see what the app does. Probably use a count of 1-and-2-and-3-and-4-and for normal [4/4] [each count is an 1/8th note, 1-and = a 1/4 note] or '1-and-2-and-3-and' for a waltz beat [3/4].
I have absolutely no background in writing music, but, I think your 1st step is to make 2-3 recordings. then determine the average note length, just counting 1-2-3-4 or 1-2-3, 1 and 2 and 3 and, etc., You're working backwards plan. You may be able to make a rough guess by counting as you play. Then see if you can find a timing pattern to fit 3/4, 4/4 etc., to set up the measures. I think using a metronome may be too restrictive.
'Block or street gathering [party] day' for dulcimers on an annual basis.
@dan 
Or 'MD Day".
OK for me although 'Appalachian' sounds a bit 'puffed up'. Reason, I'm used to referring to it as a mountain dulcimer .
Baaaaaa
{No need for a poll.}
Turn them over and make new notches. If it uses a 0 fret just open the slots so he bass string fits will usually work since the nut is for lateral string positioning. Or, you could just play the bass string as the melody [DAd] like a friend did.
@richard-streib Any date that is usually mild in both hemispheres.
Length of day/night [equinox] is irrelevant and is assuming everyone can, or will, take time figure out the right date. It's easy to mark a consistent date, or day, on a calendar.
I'm really the right one to talk about dates [sarcastic], I usually remember about an event the next day or forget about them entirely. 
How about the last Saturday in March? It's not a normal work day and is early spring.
This could whole thing could result into some really interesting posts.
"I'm going to a Dulcimer Fest on ADD [Appalachian Dulcimer Day]. I'm taking a class from a instructor who wants everyone to bring a CAD [Chromatic Appalachian Dulcimer]. He says he uses a LD [Lap Dulcimer] with all the frets. I'm going to bring my matching MD [CMD] and a friend is going take their AD and tape on some toothpicks".
When I was introdued to the instrument, it was 'Mountain Dulcimer'. I still think of it that way [or MD]. The other names came later, in some cases, much later. Bill will always be be Bill, not William.
I kind of feel there is too much overthinking going on. Much of the time it is called an MD, or Dulcime[o]r on this site. On the old ED, MD, or Mountain Dulcimer vs HD, or Hammered Dulcimer. I think most general references in news articles, Mountain Dulcimer is most commonly used [probably wrong, but ].
If we commonly refer to it as a MD or Mountain Dulcimer internally [ FOTMD], why use a different name for a special day in it's honor?
Although it would probably be nicer to have it sometime during the late spring to early fall.
No on the tunings, yep on random, just pick any day, the 3rd friday of any month, 2nd blue moon, or any other random day. Don't bother trying to make some kind of association with the dulcimer, that's not relevant.
I feel associating a particular date with a primary purpose of celabrating the overall appreciation of the MD is kind of restrictive. Almost all of the posts refer to subsets of the main subject, the MD. Just picking a random date [the 164 day of the year] and calling it 'Dulcimer Appreciation Day' or something makes more overall sense. Then all of the things expressed are valid subjects for inclusion.
'Jean Ritchie Day'.
Why tie it to some specific dulcimer event which could be the name anyway? Like 'Jean Ritchie Day' or 'Kentucky Dulcimer Day', etc.
The 'why' the day was selected is irrevelant, just as long as a day is identified and observed consistently.
I suggest the same day as 'play music on the front porch day'.
Aug 1 is 'Uncommon instrument Awarement Day'. 
It could be that the MD is particularly resonant to B, which makes that note 'stand out' more. Since you are trying to play the tune in Aeolion [capo at 1] mode it may work to try tuning to DAc.
Sorry, I forgot to say to set the bridge to the same measurement as fret 1 to fret 8.
You could try tuning the bass string to C on the 7th fret, position a nut, then tune the melody open to the bass 7th.
Fixed 'do' and movable 'do'.
Fixed,'do' always = C.
Movable, 'do' depends on scale used.
To be clear; The notes for DAd are D3A3d4, much higher the strings break.
Another source of strings;
https://www.stringsbymail.com/
I've used both
Here is a short video about tempered tuning that may be of interest, especially to those of us in the learning mode. It was presented on another site [autoharp] and I'm 'borrowing' it.
A floating bridge is one that can be moved across the top of the fretboard. The other bridge style fits into a slot. Since you're asking I would think you're MD is set up for a floating bridge. Use your tuner to adjust it to the proper location. Tune the open note, check it at the 7th fret, if sharp, move the bridge away from the nut and repeat
It's not necessarily a kit. It may be a modified kit, made from scratch or with made from a variety of purchased parts.
