An argument could even be made for using a second period to close the outer sentence after resolving the inner sentence and the quote.
Dr Johnson kicked a large rock and said, as his foot rebounded, “I refute it thus.”.
This looks weird to me because it’s not what I’m used to, but it makes logical sense.
Surely the story would be more believable if the POV character endorsed green rather than blue. As it is, I don’t find them a very sympathetic character, and I can’t imagine a reasonable audience would either.