I finally managed to get through to the folks at Singer, and the lady on the phone was very helpful. Turns out, my serial number was under the machine, on the flat part of the edge, but the paint had bubbled up so much that I had to scrape off some of the rust (white powdery crap) and take some nail polish remover to get the rest off with the little bit of paint that was left. The number was not on a plate, but engraved right into the bottom.
Officially, my machine was born on November 6, 1956, in Scotland. Website says Clydebank, lady on the phone said Kilbowie (or something like that)
Aparantly there were not many of these machines made, and they're even less common in black. I still have no idea how to figure out a value, in it's current condition or before the damage. It was in great shape, with no wear to the gold paint or black paint or anything... :(