This is one of the most boring, frustrating, stupid missions I have ever played on STO, which is what I have come to expect with all their ground missions.
The fleet runs all the projects when they're available. Problem is provisioning projects aren't available when they're needed so members are forced to wait needlessly on stupid game restrictions.
I have the same experience. I equip my weapons batteries on my tray but I only get to use them once before they disappear. This does not happen to my shield batteries.