Thank you gentlemen. Skip is right, I know what the music sounds like. And the recording ability of my phone should be good enough. I am just archiving at this point in time.

As Skip sez, you don't need concert hall audio quality at this point.  A free audio recorder app on your phone is more than adequate to trigger your memory for what a tune sounds like.  

I wouldn't worry about 'audio quality' right now [you already know what it sounds like], you're just trying to archive the tune.

I need the note values (or at least think I do) because from day to day when I play (sometimes), things sound not quite right and it takes me a bit to remember the way a piece is supposed to be. I am working with a mild to moderate aphasia,  Memory and recollection just ain't what they used to be.

Agreed on the recordings. But until I get a decent mic to use with my laptop, any recording has close to zero audio quality.

Definitions,,,

Fingerpicking is one way of playing the notes of a tune.  You can also strum or bow the string to sound the notes.

Fretting is choosing which notes to play  -- either fretting single notes on the melody string (Noter & Drone or Finger dancing) while the other strings drone;  or fretting any or all strings to create chords.

Question -- if you have your "finger positions copied down"  why do you need to assign note values?  99.9% of dulcimer players are accustomed to playing from "tabulature" -- three line number sequences showing which string to fret when -- rather than the half/whole/quarter notes of Standard Music Notation?  Everyone who creates tab has their own method of indicating time -- dots between numbers, long and short spaces between numbers, etc.  Simple recordings of your compositions would seem to be the easiestway to recall "how to play" a given tune.  

I am playing by finger picking. While I do 'fret' chords, I might play any one string and/or move up or down a fret or two as the melody dictates. The one-and-two-and suggestions are excellent. See, I am coming at the playing in a strange manner. I am recovering from a pretty massive stroke. I had the true luck of OLYMPUS, because I am not drooling on thee floor in a corner someplace. I have been truly Blessed. It is hard for me to ;earn songs, but strangely, 'composing' is much easier. Whether there is any good coming of the writing is yet to be determined. Certainly not by me, eh?

The ideas I am getting here are pure gold to me.

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].

Are you playing Chord-Melody style across all the strings, or just working out a tune on the melody string?  Either way, there are tables which tell you what note each fret has in each tuning.  One to check out is the Strothers Chord Wizard -- Tom & Missy Strothers | Diatonic Chords   to help you figure out wht is what.

~L~ No music background here either. Just about enough to see 'notation' and suss out the time. Desperately trying to remedy that. Then maybe punch it into TablEdit or Musescore and see how the playback sounds. TablEdit will do the work with a "MIDI" input device. That may also require a licensed version and money is just too tight to do that right now.

But I do like the 'counting along' idea, thank you very much.

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.

I have been doing a bit of original/creative things and I use a "notation-tab" sheet from Folkcraft. (Excellent product, I highly recommend)

While I have finger positions copied down, I am still relying on memory the be able to go back and play them.

I need to assign note values. Any ideas, suggestions or 'son, yer on yer own...', thoughts?

Maybe use a metronome and work backwards?