This is a neat project! The statistical test used could be a lot more sensitive, by taking advantage of information about the physics of biased dice. They test whether 6 is rolled more often than it should be relative to the other 5 numbers, but they should instead look at whether it's rolled more often relative to 1. Since these are on opposite sides of the die, and unfairness in 6-sided dice comes from uneven distribution of weight, these go together; you get to combine the information from too-many 6s and too-few 1s and get a test that needs only about half as many rolls to reach a given confidence level.
Originally, I was going to point out other null hypotheses that we could try to reject. This has the advantage that some of them (like the one you propose) model the physics. And it also has the disadvantage that if we propose too many hypotheses to test, then we will be more likely to get false positives. But the article was already too long, and this is a HUGE can of worms to open.
