Since you've got a reasonable antenna, the other elements in this, from a history of post-processing geodetic measurements, are proximity to the tower and height above ground. The zephyr appears to be an enclosed calibrated ground plane reflector, with a similarly calibrated preamplified patch antenna. Reasonable design, been in use for decades. A choke ring might mitigate multipath a little better (I used to question some of that contention with Gerry Mader, antenna geek extraordinaire at the National Geodetic Survey).
Trimble has always claimed to have advanced multipath mitigation but urban canyon geodesy taught me they had better marketing than factual content until you got to the choke ring antenna (Mader was right) but it was better for incident multipath from above and sides than from below. Your position above the roof suggests it's likely to see reflections from whatever is nearby and below. Ground planes also are prone to some knife-edge diffraction. Nearby trees will almost certainly be in the far field and likely not contributing to multipath so much as absorbing signal when they can. Of course, the tower is likely a multipath contributor. Still, getting sufficient data to derive cross-arm azimuth shouldn't be a big deal for dual-frequency resolved data.
The coax is likely not contributing to much beyond lower signal levels.
One thing I recall is that Trimble liked high power preamps, They were working, back in the bad old days, with 45 dB preamps, and testing with 2 Trimble receivers and preamplified antennas side by side tended to cause ringing between the antennas! Based on published specs, I suspect they're still doing that. I doubt that's an issue here with a completely different manufacturer's antenna; Ashtech antennas didn't cause ringing when used in tests close to Trimble hardware.
For what it's worth, we did have a pair of antennas on a secure mount on the roof of the building where the geodesy lab was and collected L1 data for differential corrections, and L1/L2 RINEX to support CORS, and for local campaigns where we'd process against its long-term derived position (which was pretty bad vertically, and changed with each heavy rain).
The work I did that led to the rewrite of NGS-58 was done with both Trimble and Ashtech receivers, and Trimble ground planes and Ashtech choke rings.
gc