Many centuries ago in another galaxy I was in the same situation; I had applied 3 times and completed 2 years of college before reporting for I-Day. My experience may not be yours but this was my thinking at the time. My burning desire was to be a Navy pilot sliding down the approach path on a wet crappy night to a greasy, slippery deck of a pitching carrier with my hair of fire and hand on the throttle. To me the Academy was the best way to get to that ejection seat as I wanted to be the best jet jock and best officer the Navy could turn out. As a result of that desire, the 2 years "extra" in school really did not bother me as I considered it the same time I would have spent getting a masters in leadership in Civilian U somewhere. Also due to some stupid decisions, I was coming up on the end of my sophomore year at Civilian U short of credits so I was on the 5 year plan already. My appointment came at the right time. I also found my years at college was a tremendous help in terms of maturity, study habits, ability to express myself in writing. I also detested being broke at a civilian school and working my tail off at minimum wage school and summer jobs to pay for life really sucked. As my 4 years at USNA came to a close I also found myself absolutely sick of school. The grind of read-study-test-read-study-test-read-study-test was driving me nuts and I hungered to just get into the fleet and just do a grown-up job. I had NO desire to ever sit in class again which certainly included grad school.
You may well be in a different spot. If you are still on a solid 4 year program AND you are hot for that ejection seat above all (you talk about grad school) you may well want to kiss USNA goodbye and go for AOCS or NROTC. While those routes are a bit more iffy for active duty (meaning that getting in them may be harder in the first place, not that you would not go to active duty) they would put you closer to a carrier deck than USNA. You mentioned grad school. In order to be promoted to senior rank in the Navy you will, indeed, need some sort of grad school and when that time comes in your career (around LT or LCDR) you will be well aware of all the opportunities that the Navy offers and I am sure other posters can fill in what they are. However, the Navy does not like to educate Reserve officers as they are the first to be cut in times of draw downs so your first challenge is to become a Regular (as USNA ensigns are) if you want the Navy to pay for any advanced education. That can be tough as great Reserve officers are forced out when the money starts getting chopped and depending on rank, fitness reports, needs of the Nav, they may let very few Reserves augment to Regular. Many of my Reserve officer buddies did grad school on their own on weekends and late nights during shore duty at their own expense. Some wanted to make themselves more attractive for augmentation and some were planning on getting out anyway.That is also tough with a young family---marry a good woman.
So taking all that into account, maybe you would take on USNA , even after 3 years of college, if you love studying and come out with a master's or close to it. By the way, I never got my F4 on a rainy night. My eyes went bad as a Youngster and the rainy nights were spent on the bridge of a destroyer. Nice you have a backup.