NavList:

Tom Patrick, you wrote:
"I looked at that star chart and found two pairs of stars with the same RA (or SHA). "

Perfect! That's exactly the way to do it! Any pair of stars with nearly the same RA can be used to locate the local meridian. If they are vertically aligned, that's the meridian. The pair that you used h UMa and θ UMa are unremarkable third magnitude stars, but they're easy to identify since they are part of the standard delineation of Ursa Major, going back at least 2000 years (Ptolemy's catalogue calls θ UMa the "star on the left knee", for example. I should add that we don't need prominent stars for this trick --merely identifiable stars. Any view of the sky looking generally north or south (or toward the zenith) can be locked down to the meridian by looking for pairs like this.

Once the meridian is found, then the latitude is not difficult, especially in a case like this where we can see something approximating the horizon. As you noted, we need an angular scale first, and the best way to do this is with a pair of stars near the star we will be using for latitude. In fact, you could have used your pair from above. 

You added:
"I decided to subtract 0.2 degrees for a guess on height of eye and refraction correction. Sound reasonable? "

Well, it worked! So that's reasonable. :) In retrospect, looking at the photo and the "lay of the land" on that small island, it does seem like a good choice: 2' for refraction, and 5-10' for dip would be reasonable so anywhere from 0.1-0.2° net correction.

One note for any future analyses like this one: You mentioned you got the declination for θ UMa from Wikipedia. That's not going to be significantly wrong, but the catch is that this is the J2000 declination (it says so at the top of the info box on the θ UMa page). What we want is the Declination "of date", like you would find on any of the daily pages in the official Nautical Almanac (but not this star!). You can find that in many apps, like Stellariun. Oh but there's another catch... when was the photo taken? If it was taken in 2000 (unlikely) then your Wikipedia coordinates are fine. If it was taken two or three years ago, then you need the Dec of date for that year. The change from one year to the next is insignificant for a photo analysis like that but five years would make a difference. All that side, never mind those "catches"... Your analysis worked! :)

You concluded:
"Something called 'Three Standing Stones'. A sort of unfinished Shetland Henge maybe? I couldn't find anything more about it."

Yes, that's the spot! Nice work.

As for its origin, it seems we have only local lore. Is it ancient? That seems unlikely at this point, but small "monuments" like this are common in that part of the world. Equally possible is a "folly" (built by some local decades earlier to 'echo' ancient monument style) or just a bit of fun! One suggestion says road workers put the stones up (for fun?), but this seems to be no more than "anti-lore lore". The best evidence for that latter model would be a "before" photo from some years ago with no stones present. But it doesn't really matter, right? To quote another Wikipedia article focused less than five miles from those 'three standing stone' --but still among the Shetland Islands... "nobody cares". 
[looking for more fun? find that Wikipedia article! And then maybe connect it back to another non-astronomical clue I included in my original setup for this little puzzle]

Finally, this is now a well-known story, but for anyone reading along who is not familiar with this origin story, the name Dnoces is a modern alternative name for Talitha (iota UMa). Dnoces is "Second" written backwards. It was a bit of graffiti from the Apollo 1 crew (created before they were killed in the Apollo fire in 1967) and it was a tribute to Ed White II (the Second).

Frank Reed