Looks like Saint Sheldon was right, but elsewhere. http://www.sheldonbrown.com/schwinn-braze.html says under 1962 to 1978: Schwinn Fillet Brazing In the Bicycle Boom
The fillet-brazed CrMo frame construction of Schwinn's second class of lightweight bicycles - the Superior, Sports Tourer and Super Sport - was unique. The production flow for these bicycles began with frame fabrication in the handbuild part of the Chicago Schwinn factory; a low-volume production area. Frame tubes were mitered in a jig by machine, and then the remaining fabrication work (brazing, filleting, braze-ons, and finishing) was done by hand. The seat and down tubes, as well as the top tube on the largest frame sizes, are slightly oversize at 29.5 mm in diameter. Schwinn called this tubing "1 1/8 inch diameter."
You will be hard-pressed to find a new FD for cheap these days. Modern components tend to be more 31.8 or 34.9 mm.
Your best option will be to find a used 28.6mm on ebay and carefully file the clamp to fit your tube profile. A 25.4mm FD would just need a lot more filing to achieve the same fit.
A less-pretty option would be a 31.8mm clamp and then shim it out with a lot of additional material, but that will be uglier, and potential flex under tension will make shifting worse.
You could also use a braze-on adapter and a separate FD mech.