First question: Have you or your parents run the NPC for Rice, or are you fine being full pay without taking on any debt?
If budget is not an issue (a big “if” for most of us), then given that Rice is clearly your top choice, it makes sense to apply ED.
However, Rice is a reach for nearly any student. An unweighted GPA of 3.7 is very good, but still leaves Rice as a reach. You should be thinking about other schools to apply to. Think about what you like about Rice, and look for other similar schools. There are a LOT of very good universities in the US, and you will get into some very good ones with your stats as long as you are careful to apply to safeties that are affordable and are a good fit for you.
Between Rice, Emory, and Vanderbilt, none of these three are safeties.