One thing those of us in leadership roles can do is to keep an eye on which doffs people aren't parting with easily. I personally will avoid slotting anything with green security doff requirements from here on out -- which makes sense, as security contains a lot of pricey doff specialties.
I think it's also notable that there's an overlap in what our current pair of jammed up projects require. One requires green assault squad officers, the other any green security doff (including assault squaddies). Because people have to choose which project to donate assault squad officers to, we're "splitting the vote," and neither project is getting done. So another strategy I think fleet leaders can use is to consciously avoid that kind of overlap in requirements.
When this situation does arise, I think all fleeties can help by prioritizing their resources wisely. The project that requires assault squad officers drops 500 XP and some provisions that we already have in spades, while the project that requires any green security doff (assault squaddies included) drops 1000 XP, advancing the starbase twice as quickly. So it's best for the fleet if everyone puts assault squad doffs into the 1000XP project.
Another thing to keep in mind is that I thiiiiink the different personnel officers are focused in different disciplines. The Andorian officer at the academy, for instance, is more likely to drop red-shirted doffs like the ones we need, if my theory is correct. So if you're going to do reassignment missions (trade in commons for uncommons), use her to improve your chances at the doff the fleet needs.