It was a good article and I have also heard both stories. The first is, I think from Nakayama as he tried to find some da vinci code in shoto's poetry. The second , Hoan Kosugi and the tora no maki is fact , though, traded for the kata Kushanku I think. Funakoshi later taught Kanku-sho and dai. " The half Moon ' Is the symbol of the JKA , who ever designed the patch wanted to give a shout out most likely. Hope some of this helped and really liked your article