Oh, and Chekhov did mention the department store encounter between Jodie and Okiya. If Okiya is really Akai and supposing we can trust
Jodie's hunch that Akai did indeed write the warning, it might also fit, seeing as Okiya was shown as being present prior to that.
(Although scar Akai could theoretically have written it as well, but even so, the scenario would also fit supposing Okiya = Akai)
edit: Oh God, if you actually read especially the department store case with that thought in mind, some things just jump at you; what I found very prominent was
Kir talking to Gin about her killing Akai. If you read it while at the same time supposing Akai is alive, it seems almost like Kir's having an underlying mocking tone, knowing he's still alive - although we can't be sure Kir is actually in on the plan, if there was any.
But IF there was one, I think it's almost safe to assume Conan played a (major) part in it, which would again fit with Kir's reference to "a genius mind like Holmes'"