I have a V-dipole (120 degres) working for some time now: https://network.satnogs.org/stations/2220/ which faces south.
And I’m wondering if changing it to a turnstile would result in worse quality of satellites on polar orbits directly over me while gaining omnidirectionality?
And btw congratulations on building such an addictive service, I really enjoy vetting the waterfalls.
Turnstile and Eggbeater models give you circulair polarization and that can be an advancement when receiving signals from a source (satellite) that is rotation, tumbling etc.
And one other remark, satellites can also have antennas that are circulair polarized like the NOAA satellites.
Here an example: https://youtu.be/nvC28YCnSok
A good EggBeater source: https://on6wg.pagesperso-orange.fr/Page%201.html