Besides it's God rest YOU merry. It takes the objective case, YE is the subjective."Y" in english came from anglo-saxon "G" not "TH". There are a hundred words and more which in German have a "G" and in English a "Y" -- gester/yester(day), tag/day, etc. "YE" was never pronounced "THEE" -- "THEE" is the 2nd person singular objective; "YE" is the 2nd person plural subjective.
Alex