I'd note that increasing actions is unlikely to actually fix the problem, just hide it better and exhaust the GM faster. Well proven across SB and SV quests.
What you need with a Primarch is increase the power of actions. They are extremely badass and get a lot done, but they can only be in one place at a time. This maintains the challenge of choosing which fire to put out, but wherever the Primarch hits the fire IS going to be put out, unless its outright impossible without primarch work.
I'd suggest a restructure as below:
-Research shouldn't be conflicting with other choices. Intellectual Primarchs like ourselves, Magnus and the like SHOULD always be doing one research automatically every turn just from thinking about things in transit(a battle barge is hardly a car, it can have proper labs if a primarch wants labs). If we were at peace being able to trade actions for more research makes sense, but we're at war and constantly moving, so theres no sense in doing so.
-Socials given the Warp shouldn't be open selection. Just bundle socials into deployment actions. The Primarchs are all too damned busy to take a separate trip just to chat, make it an event vote after choosing deployment, where you can get anyone in that theater or an adjacent one into one scene. Plus a semi-random one where other primarchs might seek us out.
-Infrastructure same as research, any administrator primarch SHOULD be able to delegate the build orders, they only need to indicate what priority is going on.
So I'd suggest the following example turn plan:
-Research Focus(Pick 1)
--<Insert research options>
-Administration Focus(Pick 1)
--Improve Infrastructure
--Uplift
--Cult hunt
-Force Deployment(Pick 1-3, divide forces between them)
--<Insert list of locations to intervene with Legion>
--Pick one of these locations for the Primarch to physically be present for.
Force Deployment triggering subsequent social vote for whoever is in the area.