Just a note about the crafting levels, they are based on difficulty not commander level. Hard will always be lvl 40 enemies no matter what your commander lvl. From memory the drop rate is Commander 1-15 Easy, 16-30 Medium, 31-50 Hard. So you start getting lvl 40 Hard missions as early as lvl 31 commander but they will get easier as you lvl up your girls.

Having said that, The drop rate on the schematic (2% for RANDOM 5* emblem) means that on average it will take you one and a half weeks (3 invasion days = 18 invites = 54 missions) to have just 1 drop. The cost of 6000 shards is not as bad as it seems because on average you will get 300 per invite so you should end up with way more shards than required.