Just an update. The 201 has many parts soaking to get crud off of it. The previous owner smoked (and not just tobacco) and the machine smelled of it. It's also the greasiest machine I've ever worked with,.... or was. It's just awaiting a good cleaning of the body, then all of its parts will go back on, then a good oiling / greasing / polishing.
Before I disassembled though, I test sewed to see what I was dealing with. I'd say a small tension adjustment in the bobbin area is all it needs. Otherwise, it was a perfect stitch, and so quiet!!
The only thing so far that's really challenged me is getting the bobbin case out. Singer's instructions are terrible, so I'll give the TFSR method a try tomorrow.