I'd like to suggest some changes to officer generation given the upcoming changes to officers and the additions of extra billets
While you've said that you want to limit the availability of senior officers to try and keep the amount of full officer crews low in most ships, and that would likely work to a degree, I'd like to make another suggestion based upon what I see as the real sticking point; that being that officers START at LTC, which is the naval equivalent of major in the army. However, with the introduction of all of those division heads on board a single ship, it is highly unlikely an officer that highly ranked would be heading all of those divisions, extremely so on smaller vessels or non-combat vessels. For example, the ChEng on most non-cruiser vessels would likely be a Lieutenant or a VERY junior LTC, and the TAO definitely would, or perhaps even a senior LTJG, as an example.
I would like to suggest adding in Lieutenants to the naval rank system as the rank at which officers spawn, as they are far more likely to be filling most billets that aren't XO on most ships, and would likely be the XO many smaller vessels. I feel this would also help with maintaining officer scarcity(which appears to be a goal of yours, Steve), as there would be yet another level of promotions needed to reach higher ranks.
This may require some rejiggering to the military academy spawn rates, however, or a change in the promotion metrics for officers so that it isn't a pure 1:3:9:27:etc ratio for all naval officers. One other suggestion I'd like to make, if you do introduce these changes, is that, if it is feasible, would be to reduce the amount of experience gain for lower ranking officers so that they don't become absolute monsters by the time they hit commodore or flag rank.
I feel this would also be more realistic for fighters, for example, as you'd probably see LTJGs or LTs in command of them, instead of LTCs or higher. LTs would also be more likely to be staffing actual staff positions in administrative roles along with LTCs, meaning that you would be able to compensate for the lower level of LTCs by employing more LTs in staff positions.
As an example, using the future rules and my own (near endgame tech) level DesRon, all vessels in said squadron are 12000 tons, and would likely have all relevant officer slots open (XO, CHENG, TAO). The problem being, though, that these are still Destroyers, and the smallest ships I deploy in a main combat role. They aren't commanded by Captains, but Commanders or Lieutenant Commanders. Under the revised rules, I wouldn't be able to fill those billets without inflating the ranks of my ship commanders, unless LTs were added or I built a whole bunch of academies to flood officers who would never be assigned anywhere to make up numbers, because I don't have a giant navy overall, and those senior officers are used in staff positions or commanding much larger vessels, which I find completely unintuitive and not quite in line with Aurora.
On the other hand, if you do want to keep officers solely at the "senior" level of LTCs and higher, then perhaps instead of requiring officers in all billets for all ships, have some kind of graduated size cutoff or checkbox for those modules, where instead of a named officer, a junior officer is the one in the position, with a flat (and low) bonus that never improves, unlike an actual named officer, or just go with directly tweaking the promotion algorithm to keep flag officers rare but increase the numbers of mid-level senior officers.
Another option, depending on the variables involved, as well, another but more complicated idea I had was that only the "promising" LTs would be available for actual assignments, instead of all of the LTs in the empire, but I'm not sure how well the code could handle only "promoting" the special LTs into existence for assigning to things rather than all LTs as the new bottom rank, with them being promoted to LTC independent of the normal promotion rules.