I'd guess the Nashbar brakes are short reach- they would mention the fact if they were "long" reach. They're actually Nashbar-brand Tektro brakes, so you can get similar calipers from Bike Tools Etc.:
http://www.biketoolsetc.com/index.cg...em_id=TK-R350F
Short reach probably won't fit- 80's bikes were usually long reach, which means you need these:
http://www.biketoolsetc.com/index.cg...em_id=TK-R356F
or even these:
http://www.biketoolsetc.com/index.cg...em_id=TK-R556F
I put "long" reach Shimano 600 (single-pivot, pre-Ultegra) on an '80's Schwinn Letour that I converted to single speed and straight bars. They work fine, and it's a great errand bike.
You doubt Sheldon's instructions? Be gone with you!
Jeff