I went back and looked at the game logs and every single one of Koji's April and July appearances he was throwing to Hanigan, and all of his other appearances he was throwing to someone other than Hanigan.
Hanigan 113 splitters, 36 fastballs (75.8% splitters)
Non-Hanigan 167 splitters, 154 fastballs (52.0% splitters)
I'm with you on small sample sizes and jumping to conclusions, but while it's a small sample in innings, 149 and 321 aren't small samples in pitches thrown when looking at a mix of only 2 pitches. Additionally, the buckets aren't arbitrary, we're talking about different catchers putting down signs. Have I looked at the film for all of these games to actually check which sign got put down for each pitch to see which ones Koji shook off? No, but I'm comfortable saying that in most cases, he doesn't shake it off and throws what's put down, and thus, that Hanigan calls more splitters than the other catchers on the team.
Anyway, whether Hanigan is truly the reason that his April and July pitch mixes have been so splitter-heavy isn't the real question at hand. It's really about pitch mix and effectiveness, and here is what my stance has been from the beginning...
Over the course of Koji's career, the splitter has been a better pitch than his fastball, and it's not close:
Whiff% - Splitter 25.14%, Fastball 12.42%
Whiff/Swing - Splitter 41.25%, Fastball 25.33%
GB/BIP - Splitter 43.43%, Fastball 21.08%
HR/(FB+LD) - Splitter 8.07%, Fastball 11.57%
BAA - Splitter .173, Fastball .213
SLG - Splitter .286, Fastball .414
ISO - Splitter .113, Fastball .202
If Koji is going to throw one single pitch to a random batter, and you're picking which pitch it is, you should have him throw a splitter. I think that everyone can agree on.
With that much of a difference, game theory would suggest that he should try throwing more splitters. As I said from the beginning, I don't know what the optimal pitch mix is, but I'm extremely confident it's more splitters than his career mix to date. You disagreed and stated valid reasons why it might not work, which I didn't necessarily disagree with, I just felt that they didn't have a large enough effect to offset the additional benefit of throwing the better pitch more often.
So what I've really been trying to track here, is, "In the games where Koji has thrown the most splitters, has the effectiveness of the splitter been reduced, or has his overall effectiveness been reduced?" It just so happens that, coincidentally or not, the Hanigan/Non-Hanigan buckets match up very well to look at the data, and definitely coincidentally, the monthly buckets match up and make it really easy to separate the data.
I looked at the effectiveness of the splitter alone. It has increased, not decreased, in those games. That was somewhat surprising to me, I'll admit. I expected it to be about the same. But maybe throwing it more often gives him a better feel for it during the game. That seems logical to me; I know if I throw the same pitch multiple times in a row I can definitely command it better than if I switch back and forth between different pitches.
I also looked at his overall effectiveness, using K% and BB% as metrics since they stabilize fairly quickly. It has also increased, by a lot, in those games. This was absolutely expected, in my mind. He's throwing a much better pitch much more often. I see zero evidence to suggest that increasing the mix to 75%/25% has had any detrimental effect, and quite a bit of evidence of the opposite. Is the sample large enough to be absolutely 100% confident that the 75%/25% mix is better? No, but it makes complete sense in game theory, and so far, in a decent sample, the results have only validated the theory.
I thought the McCarver joke was that a home run was a rally killer because it clears the bases and gives the pitcher an opportunity to "start over". 
