The lower instrument in my photo on the left is one I made a few years ago. The VSL is about 15 inches and it has a standard string set. It is tuned to DAA, but an octave above normal - A = 440.

It has a nice sound, but I have hardly played it. I had in mind that t might be used in an ensemble for adding accent on a second verse, or whatever. I haven't had an opportunity to try that with our group.

Apologies.  My wife and I are not tech savvy and can't seem to attach photos.  But, your comments have been very helpful.  Thanks again for your kind assistance.

This sounds more like an epinette or maybe even some other instrument than a mountain dulcimer (a ukelin, a psaltery?). The length of the whole instrument is 17"... that is reeeally short. And we don't even know the scale length. Is there any possibility you can attach a photo if it here?

Doubling the octave (7th fret) is a good way to estimate where to start from, but on an instrument that small he will need a lot more fine adjustment to the bridge beyond that.

In terms of where to place the saddle, double the measurement from the seven fret.  I think John was dead on with his estimate of VSL.

While I agree with your sentiment of not overthinking it, Matt, a micro dulcimer does warrant extra consideration.
We don't even know his VSL or what he considers "standard" so surely some complication is required.

If you wish to use regular strings, you will need to tune them one octave higher than a standard dulcimer.  Don't make things too complicated.

1) If you were to use normal strings, you would want to tune them higher than normal. If you were to tune the strings normally on an instrument that is too short, the strings won't have enough tension, resulting in a floppy feel and a weaker sound. A common tuning for short scale dulcimers using normal strings is to tune up from D to G. This would be Gdd or Gdg, rather than Daa or Dad, but you may need to tune it even higher.

2) if you want to play in standard tuning, you will need strings of a heavier gauge than normal.

3) This is a bit more complicated of a topic that may require more nuanced explanation, but this is the process that I personally use:
First, measure the distance between the nut and the 7th fret. The VSL is exactly double that distance, before adjusting for intonation. Make a temporary mark at this distance for your "estimated" bridge placement.
Next you will need to cut your bridge to the correct height. The correct height can be determined using the "nickel and dime" method, which is explained in other threads on this website.
String up the instrument, place the bridge at the 'estimated' correct distance, and tune up the strings. Tune the string up until it is perfectly in tune with the target note, then pluck the string at the 7th fret and note whether the "octave note" is sharp or flat. If the octave note is flat when the root note is perfectly in tune, the bridge needs to be moved slightly closer to the nut. If the octave note is sharp when the root note is perfectly in tune, the bridge needs to be moved slightly farther from the nut.
Detune the strings, adjust the bridge slightly, then tune back up and check again. When all three strings are perfectly in tune at the root note, and perfectly in tune at the octave fret (or as close as you can reasonably get it) the bridge is now in it's correct placement.

Points to ponder.... If your instrument is 17.25 inches over all, I'm supposing some of that length is headstock and tail? So perhaps we're dealing with a VSL of 13-14 ish?  Most mandolins are about 14 inches VSL [They tune G3-D4-A5-E5] So perhaps a set of mando strings could be a starting point? And you get a few spares.... Your tuning can be the same notes as any other dulcimer, but you are going to be in a HIGHER OCTAVE generally.

With your bridge placed where it looks "right", string and tune 1 open string to pitch. Going to the 1st fret and so forth, your notes should progress in step, if not, re position bridge, re tune and try again. Once you are good to the first fret, move on down and fine adjust down the line. Once you're good with one string, go and string up the rest. With a VSL this short, there is not a lot of forgiveness.

If you are able, a picture or two of this "mini" would be appreciated.

I just purchased a used four string instrument.  What's interesting is it's about 17 1/4 inches overall length.  It needs strings so my questions are: 

1)  Will a standard set of dulcimer strings suffice or should this smaller instrument be equipped with strings specifically designed for the short VSL?

2)  Will standard tuning work or should I tune this instrument different than a full-size dulcimer?

3)  It's missing its bridge so I'll have to make one.  There is no groove or anything else to indicate the original bridge placement.  How can I determine where to position the bridge?

Thank you in advance for any help you can provide.