I think you definitely have a strong package especially looking at your work experience and letters. I have no doubt with a few weeks of studying you could get your OAR up to a 50 or higher if you don't make it this time around. How do interviews factor into the application? My recruiter did not tell me anything about interviews.
Quick background: My sort of "mentors" on this process are 2 retired Captains whom both previously sat on a recruiting Boards early in their careers, and most importantly, Congressman Ron DeSantis, whom is a Naval Officer himself as well as recently being appointed to the Naval Academy Board of Visitors. Safe to say they lent me some good Intel on this arduous process.
In terms of interviews, they articulated that they really do enhance your package. Ask you recruiter for the form if it's not too late to add. The forms essentially have a rating system and ask questions about your character, work ethic, physical fitness etc. and really require them to explain in detail why they feel you are fit for the Navy. It just adds another reassurance to the Board if they want more detail on your background (LORs are great but sometimes too vague). I did 6 interviews but only used the top 3 my recruiter felt were the best. Obviously, an active duty or retired senior supply officer would be best.