Challenge: How to talk to a flat earther?

Further down the rabbit hole, over lunch I finished watching "Behind the Curve", a Netflix documentary on people believing the earth is a flat disk. According to them, the north pole is in the center, while Antarctica is an ice wall at the boundary. Sun and moon are much closer and flying above this disk while the stars are on some huge dome like in a planetarium. NASA is a fake agency promoting the doctrine and airlines must be part of the conspiracy as they know that you cannot directly fly between continents on the southern hemisphere (really?).

These people are happily using GPS for navigation but have a general mistrust in the science (and their teachers) of at least two centuries.

Besides the obvious "I don't see curvature of the horizon" they are even conducting experiments to prove their point (fighting with laser beams not being as parallel over miles of distance as they had hoped for). So at least some of them might be open to empirical disprove.

So here is my challenge: Which experiment would you conduct with them to convince them? Warning: Everything involving stuff disappearing at the horizon (ships sailing away, being able to see further from a tower) are complicated by non-trivial diffraction in the atmosphere which would very likely turn this observation inconclusive. The sun being at different declination (height) at different places might also be explained by being much closer and a Foucault pendulum might be too indirect to really convince them (plus it requires some non-elementary math to analyse).

My personal solution is to point to the observation that the declination of Polaris (around which I hope they can agree the night sky rotates) is given my the geographical latitude: At the north pole it is right above you but is has to go down the more south you get. I cannot see how this could be reconciled with a dome projection.

How would you approach this? The rules are that it must only involve observations available to everyone, no spaceflight, no extra high altitude planes. You are allowed to make use of the phone, cameras, you can travel (say by car or commercial flight but you cannot influence the flight route). It does not involve lots of money or higher math.