I have lots of machines, new and vintage. But...one I'm thinking about in particular IS post-1965, in fact, it's a 1978 Singer Athena 2010...I gave it fits, loaned it to one of my daughters for three years (she left it in storage, it's now back home with me!), but it ran like a champ then and it still does! The guy that works on my machines had one in his shop that he offered me for free...didn't take it 'cause no room...boy, could I kick myself now!
The moral of the story here is...maybe you could find one like that in good shape? It's a great machine, no problems out of the one I have so maybe you'd have good luck as well!
Anyway, whatever you decide, have fun choosing and using!