Ok, sorry this took so long, and thank you for sharing your knowledge. Here's pictures of the watch. Please understand that photography does not even toy with the idea of numbering among my skills, so my apologies for the quality of the pictures.
So, there's a watch and a watch case, with markings on both. On the inside of cover of the watch case, it says mermod and jaccard jewelry co, and 14k. Under the 14k mark are the number 45112.
On the inside of the back cover of the watch itself is a funny little symbol that I assume would mean something to me if I knew anything about this sort of thing. I can't get a photo because of the reflectiveness, but it looks a bit like this: 1$4 - only the line through the dollar sign has lots of swirley things on the ends. under that is a row of the same numbers - 45112 - and then on the next row a single number 8. So it looks sort of like this:
Inside the watch itself, the lettering reads " No. 35719 DC Jaccard St. Louis." It also has the words fast/slow on either side of a little mark that looks a bit like a compass rose, and the word "adjusted" curving around the centerpoint of the watch. Last but not least, on the second layer of clockworky stuff, there's a stamp in the metal that looks like a small shield - the same shape as the USDA shield.
There was no screw or anything for the back, it just opened like a lever.
This is the place that was recommended to me in our area, but someone who has taken jewelry there: http://www.timekeepersstl.com/index.php/services