Finally beating all these sources of noise down.  Several more where located.  The nastiest was from the -5 volt power supply.  The charge pump in the MAX735 was pulling considerable current, all in pulse form.  This noise was probably the single greatest contributor to our ADC noise.  Some of the previous fixes only helped isolate the receiver and not fix the source of the noise.  Greater isolation to the +5VF supply did the trick.
     The MAX232 IC's, one on the main board and the other on the Axiom, were also adding some noise.  The one on the main board really didn't affect much because of the good ground plain.  Added another by-pass and that killed anything that its charge pump was doing.  The MAX232 on the Axiom PCB was a different story.  It was a real noise generator.  Big 100KHz stuff.  Being that we weren't even using this IC in the application the best fix here was to just disconnect the power supply feeding it.  No more noise.  The ADC system is working great now.  Solid readings with virtually no jitter.