You're way high.
First off if you refresh the node you'll average 3.33 shards for your 10 attempts, not 1.67. You're using the number of shards you would get if you were just doing 5. So that has your number way over inflated.
Secondly, you don't have to buy a 100 crystal energy refresh every day. If you refresh her node for 50 crystals daily, and don't farm anything else you'll have a bit of energy left over when you refresh your energy for 100. It regenerates slowly, so it can be left until the next day without running over. You won't have to refresh your energy for two to three more days. Just her node daily. So you could farm her node 10 times a day only refreshing your energy twice a week approximately.
So by that method you should average 24 crystals per shard.
(50x7)+100+100=550 crystals spent per week
550/7=78.57 crystals spent on average per day
78.57/3.33=23.59 crystals spent per shard on average
