Hooray for the oil soak method! I finally got the back slide plate off of the Domestic. (Also applied elbow grease in the form of a screw driver and repeated jolts from the heal of my hand). Need to do some more soaking, and a bit of steel wool work, and it'll be fine. Nothing serious.
Changed stitch length and presser foot pressure. Now, get a good stitch with occasional dropped stitch. Good productivity for my lunch hour. Looks like minor adjustments from here iron cleaning and major cabinet stripping and this summer.
Still need to find accessories like feet, front slide plate, attachments. I'd also like to know how to date this old girl.