I am sure you have already viewed the USNA 2019 class portrait.
http://www.usna.edu/Admissions/classPortrait/
Half of the class had SAT scores in the range of 1210 to 1360 (combined math and verbal)
Converted to ACT the composite would be 27 to 31.
You already know your strengths and weaknesses. And yes you have a shot.
Also, having 3 nominations is better than zero.
The wait is brutal and for many will continue through the March.
Keep your head up and get those plan B and C in place.
P.S. Some college application deadlines are today and through the weekend. Make sure you don't miss those.
DS is committed to attending USNA, I just hope they agree. His desire has negatively impacted his motivation to get his other college applications completed. He completed two applications yesterday that were due today, and he has 2 more to complete before Monday.