On a longboard, you'd typically tack. If you have a decent longboard and halfway decent technique, a typical polar plot would show pretty high board speeds almost straight into the wind. You'd have to exclude turns, but the timing is quite different from shortboards, since the longboard turns more slowly.
In a session like the one posted by thedoor, it's usually pretty easy to get a good idea of upwind angles by just looking at the angle between two upwind legs. There are a couple of 90 degree angles, but those are probably in downwind legs. The longest leg shows an angle of closer to 80 degrees (just eyeballed not measured), so that's point about 40 degrees into the wind. Quite good, but about 5 degrees less than what I have seen in longboard race tracks.
Anyway, if something like polar plots for low speeds are important to you, feel free to post it as an issue on the GPS Speedreader projects on GitHub (
github.com/prichterich/GPS-Speedreader/issues).