I just noticed it's been 6 weeks since I last posted. Oops. Thing #7 was completed long ago, but here's the update. More Internet searches were unsuccessful, but then I joined "theportabletypewriterforum" Yahoo! Group, and after posting a query to the group, had my answer almost instantly. Not only did they point out where the serial number was located, but someone was kind enough to send me a PDF scan of the manual for my typewriter.
So. I am the proud owner of a 1962 Smith-Corona Galaxie, deluxe portable manual typewriter.