Not a fan of the current officers system either, but I have a little idea, which I think makes sense in real life and it is lore friendly too. So bear with me, please.
All these skills are based on intelligence, wisdom and experience, right? They are not like in some RPGs dependent on some physical attribute that not everybody can have - needing high strength to wield a heavy sword, high dexterity to properly use a bow, or maybe charisma for trade, stuff like that. Now, in real life, a smart person, with a bit of effort and practice, can learn a lot of stuff, speak several languages, learn all kinds of skills, right? They won't be experts in all of them, but they can be proficient in many of them. And this ties perfectly with our in game officers system - they can learn several skills, but only a few can be elite. So the game's elite skills are the equivalent of my real life experts example - we can be experts in just a few things, but proficient in many more. And officers are supposed to be relative smart, in real life and in game.
With all that said, all we need now in game is just an officers academy type of building. When officers are at max level, we can send them to these academies, pay some credits for their studies, and leave them there for a period of time (6/12 months). We choose a new skill to learn, and replace an old one, but the old skill will remain learned, just not active. When the training period is done, the new skill will be at a basic level (no bonuses), but we'll need to level it up, just like we do now with any skill, in the current system. This way we should be able train them in all the skills we want, but of course, restricted to 5-6 skills active, and 1-3 elite. We should be able to switch between the learned skills somewhat freely (no need to go back to an academy), paying some credits maybe, and some sort of cool down - not as easy as with the AI cores. Of course, Alex should do some sort of balancing.
This officers academy building should probably be restricted to one planet per major faction (Hegemony, Persean League, Tri-Tachyon, Sindrian Diktat, and maybe Independents? I don't know). Not sure if the player should be able to build it. Definitely shouldn't be an industry - I'm thinking something like the Cryosanctum.