I've sailed with MSC four times (and went through the process half a dozen more times over the course of COVID moving sailings). Every time has been a direct booking via the website and every time I've used Military / Civil Service discount. The method that works for me is:
1. Find the fare and promo you are happy with and book it direct on the MSC website. To figure the after-discount cost take 90% of the fare total and add the port charges.
2. After putting down a deposit and getting your reservation number, send an email to mscexistingreservations@msccruisesusa.com - in this email ask for the discount to be applied and attach a copy of appropriate proof.
3. Typically within hours, or the next day, a reply will come with an updated booking confirmation showing the discounted total. It's always been accurate to the penny to the expected total and all promos (free drinks, OBC, etc) are retained.
I've had my share of MSC issues but never regarding adding the discount.