Interesting - but I have a question - what did you rely on for a groundplane? I am assuming that you attached the antenna directly to the analyzer thereby using the analyzer's case metal as the groundplane, or ??
I know that the scanner's themselves provide poor groundplanes but, usually, these antennas are designed with a proper "ideal" groundplane to work with.
What I would do if I had your equipment is to setup a horizontal groundplane made up of a circular base of metal which is at least large enough in diameter to that required for the lowest likely usable frequency of the antenna; let's use the bottom of the civilian air band, 108MHz as, obviously, the antenna isn't going to work efficiently at low band and just round it off to 100MHz for simplicity. I would use a radius of about 25 to 30 inches and I would drill a hole in the middle of the ground plane and mount a male-to-male BNC panel mount at that point. Using high quality coax with the lowest loss possible up to 1GHz but compromised with practical flexibility needs for the test setup, first null out/normalize the coax loss and then attach to the antenna mount. I would then locate the antenna mount at least several feet from the analyzer (and yourself) and in as open an area as possible (no objects in close proximity to the antenna) and at least a few feet high off the ground. Then I would run return loss measurements like S11 and VSWR across the full range as you did (though I would like to see S parameters in addition to VSWR). Also, it would be nice to see more detailed plots across the bands of interest. Thus, in addition to the full range plot I would make separate plots detailing just the civilian air band, VHF-High LMR band, 220MHZ to 400MHz band, UHF LMR band, and finally 800MHz to 960MHz. These I would find interesting. I would also love to see Smith Chart plots if at all possible! If you want to get even more accurate and if you could figure out a practical mechanical way to do so, you could replace the circular ground plane with a cone of metal with slopes at 45 degrees from the horizontal so as to provide a better 50 Ohm point at resonance (the 90 degree groundplane provided by the flat circular piece of metal ideally creates something like a range in the 30's, ohmwise, at resonance). An alternative would be to use as many as possible metal rods or stiff lengths of wire, again 25 to 30 inches in length, and solder them all around the base of the BNC male-to-male connector ground ring and slope them down at 45 degrees. Use as many as possible - the more the better.
Also, if possible, it would be good to setup two separate mounts for BNC and SMA antennas rather than use an adapter. In the latter case, of course, a SMA male-to-BNC male panel mount would be used if using a BNC fitted cable or SMA male-to-male panel mounts if using a SMA fitted cable.
To provide a good baseline and establish the accuracy of the test setup, I would also provide the same measurements with a suitable high quality 50 Ohm dummy load attached to the mount point (one set of plots each for BNC and SMA dummy loads). In a pinch, 20dB or greater pads could be used if no actual loads are available.
I suspect that the GRE 800MHz antenna and the Radio Shack equivalent are half wave designs that do not require a ground plane - part of the reason for the good performance attributed to them at their designed for frequency ranges. Still, the ground plane won't hurt them and it would be interesting to see how that antenna works across the 800MHz band both with and without a groundplane. In this case, you could setup a separate antenna mount with a wooden or plastic base for the BNC male-to-male and swap it out with the metal groundplane mount. That would make for a VERY interesting plot as many have been speculating what the 800MHz GRE/Radio Shack antenna's design is. It would also be interesting to run the same tests on that antenna as run on the stock antennas just to see what the return loss is across the full normal scanning range in comparison to the stock antennas.
Another portable antenna I would like to see these plots of would be the Austin Condor - one I would definitely test if I had access to the proper equipment.
-Mike