[a humble lich]

You don't need to bother, and the part you quoted was more background in trying to explain what was going on. And there are several ways to find the time between all three moons being full, and I make no claims that what I did is the best or simplest.

On to your point, I may be missing something, but your analysis doesn't actually tell us what the interval is between full moon. We could find the percentage of time each moon is full, combine those probabilities to find the percentage of time when all three moons are full. Estimate the time when all three are full by just looking at the time Moon A is full, and then use that to find an average time between all three being full. However, I'm not convinced doing all that is easier, and looking at the graph, the time between the triple full moon varies quite a bit. An approach based on averages misses that variation.