Update: my friend found research that describes a "leaf spring", which holds the slide plate in place. Upon examination of mine, I see that the left arm of it has been broken off. I have a Golden Touch and Sew 750 that is not in good repair and ready to be disposed of. It has the same leaf spring! I will attempt to remove it and install it on the rocketeer.
She also told me that the serial number is in the metal under the lip of the bed on the left side. I haven't checked that out yet.
Thanks, everybody, for your ideas. I want to get this machine in tip top shape.