The way I see it, you will need an array and register the start time of each mod, then compare the current time against the time in the array and get the current mod.
I'm not sure about that "Every day between mods 6 and 7 there is a gathering that averages 15 minutes", but to me it looks that every day has only 25 mods, the last one starting at 2:24 and ending at 2:40