Well, dunno who is beating your head, but they know squat about antennas. There are plenty of examples of two antennas on one coax on the same frequency. Google up "phased array."
BTW, I did this stuff for a living once. People paid me very good money for it. Besides 40 years of amateur experience.
I appreciate your feedback, and I'll look into it. This is generally what I've found:
Again, I'm partway done with my 180 degree project, and if everything works right I'll just need one antenna. My locale has no surviving VHF (OK, the one VHF PBS channel has a UHF counterpart), so I only need to worry about UHF.