I am sympathetic and hope it works out but this translates into your military service commitment was irrelevant as you had mixed up the date and wouldn’t have acted before the deadline, not that you couldn’t access the means to drop based on service.
Stated differently if you didn’t “realize the mistake until after the fact” all other circumstances become somewhat irrelevant.
I hope they cut you a break but to improve your chances you may want to reconsider how you present your case.
Once again good luck and sorry for my pessimism