My recollection is that DoDMERB and any waivers are good for TWO years. Stay on top of that. DS was disqualified and received waiver for Class of 2018. He received an LOA for Class of 2019 conditioned on resolution of the DoDMERB disqualification, but once the waiver paperwork caught up with the LOA, he received an appointment to Class of 2019. I don't really know how the paperwork moves within DoDMERB, but it's something to follow if you can. The people who answer the phones there are very helpful!
Regarding LORs, my son was an engineering major and did not take a college English class. This worried me a bit. He had his high school senior year English teacher write the English LOR. One of his college professors wrote the other LOR. Regarding nominations, he pretty much did the same thing he did the year before. Scheduling interviews is a little tricky if you are at college out of town, but the staffs of the offices to which he applied were flexible, which I imagine is usually the case, especially for reapplicants who received nominations the year before. They will probably remember you if staff has not changed.
My son did not share the essay (or whatever you call it) he submitted with his second application, but I know he waited until the last possible moment to write it. Admissions won't look at your file until they have your first semester grades (we were told). So he submitted his essay over Winter break. That way, he had the benefit of a bit more maturity and self-awareness, the experience of a semester of college, and what he learned at NROTC first semester.
Key to this process is: do not be discouraged that you didn't make it the first time! My Plebe was very discouraged, but a year of college made him a better Plebe than he would have been a year ago. I also think it is helping his resolve to muscle through Plebe Summer challenges, which we are learning are significant. And those who are ROTC will report to I Day with an ability to help your fellow Plebes with some of the military specific tasks associated with being a Plebe. Wishing you all the best!