This calculation is based on a wrong assumption.
You get 165 Caninta Energy per day for free. And you assume you spend it all on cantina nodes
You get 420 normal energy per day for free. And you assume you still need a refresh of the energy? Why? is 420 not enough?
If you plan to spend 100% cantina energy for farming, you can at least expect to spend 100% normal energy for farming.
Therefore you don't have to spend extra 50 gems to refresh.
Let us see the gem cost of one shard with one refresh both.
1 Canina shard with one refresh would cost you...19 gems
1 hard battle shard with one refresh would cost you... 16(6) gems
So a 16 node cantina farm is slightly more expensive than any hard node farm.
While a 20 node cantina farm is even more expensive