Oh, and you're right, the Bayou Grande marina at NAS does not allow liveaboards, but they're fine with you staying onboard for the occasional night or weekend (we do it all the time), and they allow loopers or people passing through the area to stay onboard their boats at the transient pier, sometimes for weeks. There's a laundry room and restroom with showers available.
And I'm pretty sure you don't want to drive ANYWHERE in Florida while drunk, regardless of whether you're going through the gate at the base. The local troopers take a pretty dim view of such things.