Hi Tigger Momma
I work in policing and do the same (7pm-7am), I'm not in the military so I don't know how it works, but have you advised your superior? I was able to get mine adjusted until 2am at the latest. Most women here don't work past midnight in their late 2nd/3rd trimester. I told my boss at 4 weeks - I know a lot of women want to wait until 2nd tri, but for girls like us that work overnight, some adjustments really need to be made. It's difficult enough without the hormones raging.
Until then, all I can advise is maybe adjusting caffeine to the worst down times (maybe at the start of shift, and another usually 3am for most) and hoping for the best! Good luck!
The sleepiness WILL pass once you get out of 2nd tri, until then, you could sleep 20 hours and still be exhausted.