I also suspect the rifling will have some affect on the patterns you are getting. I have read elsewhere (for example see here: https://www.theboxotruth.com/threads...un-barrel.377/) that shot fired through a rifled barrel results in a large spread and a “doughnut pattern”.
In this case I would hypothesise that the chalk sticks don’t engage the rifling that well and so don’t spin that much. The tight fitting wad is more likely to engage the rifling and impart spin to the mass of shot, throwing it outwards. I think it would be very interesting to repeat these tests with a smooth bore barrel and compare the results.