This will probably be the last that I mess around and test this but I found what seems to be a decent solution albeit much less than ideal. I made the improvement in question <ImprovementType>Special</ImprovementType>.
I then changed GovernorDefs.xml. For every different governor entry, I inserted <Improvement>Special</Improvement> directly underneath the <PlanetClassMax> tag. Started a soak test with all the default factions that had access to the improvement I made being 5. I was hoping that would make it the 1st construction on all planets but that didn't seem to be the case. Although, about 80% of all planets for each faction had built it and all 5 home worlds had it which is many more than when I messed with it the other day. The home world I was watching did build it 1st before anything else.
I would imagine this would work for as many factions as you would want to create with their own unique building as long as it is the only Special type available to them since I assume they would simply pick 1 at random from those available.
One issue I thought of with this improvement idea is that each ship built would get an interceptor for each planet sponsoring the shipyard I think so you might end up fighting ships with 5 interceptors each.
This whole idea occurred to me when I opened up an ai thread then decided to check out GovernorDefs.xml since I had never opened it before. I usually check the related schema for valid arguments. Although they are placement types in that they seemingly reference improvement types instead and the only Special type improvements are the Colony and Civilization Capitals which are both set to unavailable.
Hopefully this is helpful to you or anyone else reading.