On a standard dual band AP with 5 GHz and 2.4 GHz radios they are only about 4" apart, sometimes closer so I don't see it as a problem.
As far as the Wi-Fi system being 4' apart from the other transmitters, all I have to go on is past experience. When we co-locate our Wi-Fi antennas on towers with other transmitters, they require that we space our antennas at least 10 wavelengths (our wavelengths, not theirs) apart. This comes out to 10 wavelengths, which equates to 50", just a bit over 4'.
Sounds like an interesting project!