I just rearead what you had on that list of wants, and first singer that came to mind is a 237 .. LOL....I have had one for a good 20 yrs and no matter what other machines I have I keep going back to that old 237...
I don't know every singer,, but a very plus on these is that ,, they do have an adjustable needle bar...
In watching C/L I notice I seldom see a 237, when I do it's very over priced.. as in a 100 plus $ There nothing more than a basic zz machine.. bolt on motor. yes made in Itlay, so can bet singer did a contract with necchi on those..