I was surprised your test was not conclusive, so I did some testing, too. I looked at the Captain's inventory and there they were, 2 hand crafted, polished air staffs (level 9) that I sold to him, both with +1 lucky charm. When I tried to replicate it (now level 14) I didn't get a single one... but now I was making superior staves. When I took off my crafting belt and went down to rank 4 crafting, I got a polished air staff on my 3rd try (had + lucky charm again).
Your observation is correct and actually not a mystery. In the game file there are several instructions for how to create staffs, one for each combination. The 8 ones that create the four staffs with or without Lucky Charm are all correct. So with Crafting 2 the 4 instructions that create them without Lucky Charm are used. With Crafting 3 or 4 the instructions that create them with Lucky Charm are used. With Crafting 5 there are 12 instructions that should create all 12 possible staffs (4 staff types x 3 bonus types). But due to a copy and paste error in the game files those 12 instructions are actually only 3 instructions copied 4 times.
