This movement is Elgin's railroad grade 252. It is a large watch, 18 size, lever-set, with 21 jewels. This example was made about 1903.
At first it looked like someone had attempted to solder on the balance cock, but I don't think the material that was on there was solder. It turned out to be very soft and it came off pretty easily - almost like a silver latex paint, but slightly firmer. Anyway, that is what was holding it together.
My Grandfather always said, you never know what you'll find when you get into a watch.
As for the screw, on other Elgin models they used a larger screw for this part. In this instance the hole in the balance cock allowed the larger screw, barely, so I was able to just re-tap the threads in the top plate to a larger size. A larger Elgin factory screw now works, and looks correct.