Some other flaws in your math:
-most teams don’t have every toon in only hard nodes
-you have enough energy to farm more than 1 toon/day from hard nodes, even without buying refreshes
-buying refreshes with your crystals is the most efficient way to spend them, and also cuts the time down (as does refreshing the nodes, since they are cheap to do).
-miscellaneous events also drop some shards, as did the marquee events (if you played them)
In other words: To make your math work you would have to be farming 1 toon/time, no refreshes, for a team that has all 5 toons in hard nodes, with no event or marquee shards to help you. And you would also have to consistently have a drop rate well below the established average.