I summarize the key paper here: Trans-Species Variation or Convergent Evolution?. Though there are many more in the literature.
Of close relevance to this, MCH Ka/Ks ratio can be as high as 10 or 12, which indicates the uncalibrated age of alleles can be as high as 10x to 12x the true age. It also indicates a high degree of selection, creating the conditions for multiple cases of convergent evolution.
No. It is not possible to interpret the MCH this way, not without much more study. It might all be an illusion caused by convergence (from common recent selective pressures). Or it might be extended or confirmed with MHC introns. Or we might good reason to think introns can’t tell us one way or another. We can hypothesize, but we just do not know yet. You are banking on the hypothesis that it will rule out a bottleneck. I have no problem with this. Perhaps you are right. Just do not present your hypothesis as a confirmed hypothesis, when it is no such thing.
So what can we say that appropriately tempers enthusiasm? We can say: "With further study, it is possible that trans-species variation will strongly challenge a single couple bottleneck at any point in human history, including as far back as millions of years ago."
I’d even encourage you to say, “the studies required to test this are difficult, so we can’t do them right now. Creationists that care about a bottleneck, however, we encourage them to do this scientific work to find out. Wee would respect and advice such an effort.”
I also emphasize that I have no dog in this fight. I personally don’t care one way or another how a study like this would go. I’m just insisting that we are honest with the public. If we aren’t, how can @MStrauss and others trust us on conclusions that are difficult for them? That is why this is so important. Do not overstate the evidence. Show intellectual empathy. Explain the evidence, but do not extend the conclusions further.