My personal view is that handing out LOAs at NASS is a mistake. First, it unnecessarily and needlessly freaks out those who haven't completed their applications. Second, some have very little hope of getting it done by NASS. For example, in our area, kids are still in school until the 3rd session of NASS. IMHO, it's MUCH more important for juniors to focus on their final exams than to complete an application that isn't due until Jan. 31 of 2018 (though, of course, it's best to submit it earlier than that).
Your best bet now is to get in decent shape so you can max your CFA at NASS and also keep up during mock Sea Trials, etc. Then focus on having a good time at NASS, learning about USNA, asking questions, etc. If you're lucky enough to finish your junior year in May, there's certainly no harm in starting your application -- but work on making it good, not just getting it done. You don't get an LOA or an appointment simply b/c you turned it in early.
Each MOC has his/her own timetable. Information on SA nominations, including deadlines, is typically posted on their website.
Your BGO won't have your information in his/her system until around May 1. As Hoops noted, some BGOs may not want to start interviewing until a bit later in the summer.