Those are all great choices, and I am a huge fan of all four (my grandfather was a Vandy alum, and my brother in law is a GT grad).
I would definitely include both Rice and GT. My guess is that Tulane’s quota might fill up early because they provide free room and board to all ROTC scholarship students. On the other hand, Vanderbilt gives $6,000 toward room and board to ROTC scholarship students, so its quota might fill quickly too.
So, take your pick between Vandy and Tulane, but include both Rice and GT. My personal favorite is Rice, and it is probably the least well known which might keep it from filling up.
Do you think that I could get accepted at both Rice and Vanderbilt? What are my odds? because they are both almost as hard to get into as Duke?
Yes, you could get accepted to any of them. I kind of doubt that you would get accepted to all of them, and it is possible that you could get accepted to none of them. I am not good at odds.
You have a better chance at Rice than at the other two. Mostly because fewer people apply to Rice. Vanderbilt and Duke are better known.
I am a Duke alum and active alumni interviewer. I agree with prior posters about your ACT score being low, esp for engineering. I also agree that you should get your backups in order, as I’ve never seen someone with a 31 get into engineering (not to say it hasn’t been done, but it’s really tough). Your background is strong and you do have a chance, but I do think you have a much better chance of getting into some of the other schools. It would be a shame not to use your ROTC scholarship, it’s a tremendous accomplishment by itself. Best of luck to you.