Well this is probably too late to help the original poster, but maybe it can help someone...
I, too, had this same question, as to whether they change the time on Enchantment of the Seas to match local time. No one, and I mean NO ONE, could give me a straight answer. However, having just returned I can definitely say that, yes, you do change your clocks twice on this ship. So, in Cozumel for example, your time is the same as local time. It seems a little weird to change your clock on night, and then set it back the next night, but that's what we did. But, it is nice, not to worry about "ship's time" vs. "local time". Hope that helps.