evilroy, what I managed to find on the book shelf re aircraft used for the "Vomit" flights, you'll note that four were KC's with a lone C. Only 15 C-135A were built (Boeing 717-157) against 732 KC-135A (a mix of 29 717-100A, 68 717-146, 635 717-148). Essentially the C was a KC that had the flight refueling gear removed but still had the boomers station, the other engineering change that prompted the different designation was the beefed up floor and cargo retention points.
55-3129 (Weightless Wonder) KC-135A 1968 converted to NKC-135A testing on board avionics, later winglet tests, 1982 reengined with TF33, 1984 converted to EC-135P for the Commander in Chief Atlantic Forces
62-3536 (weightless Wonder II) KC-135A Zero G 1967-70 converted to EC-135K May 1970 W/O Sep 1977 Crashed in steep terrain during a night time climb out of Kirtland Air Force Base. The aircraft struck a peak in the Manzano Mountains, about 10 meters below the summit. 20 fatal
60-0378 C-135A (Weightless Wonder III) with NASA 07.68-05.73, 11795 parabolas in 1120 hrs, converted to VC-135A late 75
59-1481 (weightless Wonder IV) KC-135A flew more than 58,000 parabolas 1973 - 1995
63-7998 (Weightless Wonder V) KC-135A also used to film weightless scenes in Apollo 13 movie
A full listing of variants and their uses can be found at
http://www.uswarplanes.net/kc135.html