Buy Buy - Dan Davis:

The correspondence mentioned is available online. http://ucispace.lib.uci.edu/handle/10575/1158

They seem to be talking more about Jaynes work in probability theory and statistical mechanics. Didn't see relevant comments on quantum theory, but mainly scanned the docs.

Given Jayne's interest in the foundations of quantum theory, it seems extremely unlikely to me that he was unaware of MWI. I've read most of his papers since around 1980, and can't recall a mention anywhere. Surely he was aware, and surely he had an opinion.