Here's some preliminary data. We only had 4 participants, which is enough, but more would always be better.

First, a graph of the Sun's angular altitude vs latitude of the observer:

This should show a straight line, and the Y intercept should be 90° + the Sun's declination, or about 109°. The linear fit's intercept is about 107.7°, so not too bad. The Sun's declination, for the uninitiated, is equivalent to the latitude at which the Sun is directly overhead at solar noon. It amounts to about +19° during the time of the experiment, since we're well past the March equinox.

Next, a graph of the calculated height of the Sun vs the latitude of the observer. Since the Sun was due south for all measurements, and since flat earthers use a linear interpretation of latitude, we can just assume a linear number of miles per flat earth ° of latitude, which amounts to about 110 km, and just apply a little trig to get the Sun's height:

Here, we should see a straight horizontal line if the flat Earth/nearby Sun hypothesis is true... the Sun should be at the same height for all measurements. The mean value approximates that, but the best linear fit is rather strongly biased toward some other kind of model.

Any thoughts on where to go with the analysis from here?