Won't speak for NROTC, but since AFROTC mimics in selection with the 85% going to tech, I would say you may be in for an uphill battle. Here are the reasons why:
1. AGAIN (AFROTC experience, not NROTC), the non-tech candidates typically have the same if not higher SAT scores.
Rationale for this is because only 15% are non-tech, they are fighting against more people for fewer slots. DS received his scholarship with a 33 or 34 ACT and a 1390 out of 1600 SAT.
The applicants just because they decide to go non-tech are not necessarily low scorers on the tests. Unfortunately for you, you have stated your Eng. is @ the requirement, but the Math is below, and when vying for a NROTC scholarship you never want to be at the mins since PAR is 60% of the selection process.
PAR will include your SAT, gpa, class rank, and course curriculum rigor, so you may be able to overcome the SAT issue if the rest are high. Thought process would be you are not a good test taker.
2. NROTC assigns the scholarship to the mid, but ties it to the school too.
That means as you stated your number 1 choice is a big school and with big schools you tend to have more competition, which brings it back to point 1.
Yes, they may have more scholarships, but very few mids will be on scholarship. They are actually the minority, and becoming smaller every yr due to budget crunches in the DOD.
Is the school a match, or is it a reach? That will also be a player in the equation. If it is a reach, than most likely there will be higher scoring candidates, if it is a match than your chances increase.
Is the school OOS or private, or is it IS. NROTC requires at least 1 IS college, but you do not address if you are IS. For example, you may want Notre Dame, a big school, but that is private, or you may want UNCCH as an NC resident, which would make it IS.
I am kind of shocked that they even allow Interior Design as an acceptable major for NROTC scholarship. AFROTC has limited majors, and although I haven't looked to see if ID is one of them, it would make no sense to me that they would from a career perspective for the AF. The fact is although not every major a newly minted O2 ROTC grad will match up to their career field, most of them are majors that can be used in the AF. I.E. Business can be used for Accounting and Finance or Personnel. Political Science can translate over into Public Affairs or Intel. Criminal Justice into Police force. I don't know where Interior Design can translate into, and I would suggest if you want to go this route, to take the time to investigate what career field actually exists in the Navy. I am more than willing and happy to eat crow if there is one for an O2 with a degree in ID.
PS. I do know at our DD's college there is a major that is called Architectural Interior Design. Basically you get a dual degree in architecture an interior design. That program I could see why they offer it for NROTC programs because it would equate into designing new buildings for the Navy.