My thoughts:
Before commenting on individual changes, this post leaves me a bit concerned about power creep. Feels like base unofficered ships are becoming more and more just pure fodder. Which also makes the early game balance tricker. Feels like you kind of have to run support doctrine for unofficered ships to even be useful unless they are missile spam boats or something.
Thoughts on individual changes:
Ballistic mastery seems really good with that bonus. Feels like it's on the strong side, but hopefully not too crazy.
Target analysis: I really can't see ever picking an elite skill that says do a little extra damage to frigates and destroyers. Those ships already have low HP, and die very quickly, so spending an elite skill to make you better at something that is already easy seems a bit of a waste. I think maybe something like just an extra 5% damage to all ships could work for elite. It's boring but way more appealing to me. You could also do something fancy like 5% or 10% damage to ships the same class or larger than your current ship as the elite skill, the idea being to make it a 'punch up' kind of elite skill to further enable frigates and destroyers.
Systems expertise giving damage reduction, is ... interesting? It's definitely good, just feels a bit strange. I will certainly be taking it more regularly though. Some high tech ships will be getting real tanky

Helmsmanship and combat endurance might be better now, but I'm not sure they've kept up with the other elite skill buffs. Kinda curious to see how impactful this actually feels though.
An idea for damage control/impact mitigation/field modulation:
Instead of bonus damage (which I think feels very out of place on a defensive skill), what if they reduced damage from certain damage types. For instance, impact mitigation is 5 or 10% less damage from HE type weapons, field modulation is less damage from kinetics, damage control is less energy/frag damage, or something like that? Feels a bit more thematic to me, although maybe not straightforward to implement?
Ordinance expertise nerf is leaving me with mixed feelings. I totally get that it was a bit too strong, but I really love how it opens up new builds that aren't otherwise feasible, and it's kinda sad to see that neutered. I almost wish it was just a tier 5 skill to justify its old power level. Not sure how that could happen though.
I think EWM could really just use adjustments to the range penalties. Partially because pretty much every ship has range bonuses (between ITU and skills), so while 600 range might be reasonable in terms of the base range of weapons, it's not really cutting it when your opponent is a capital ship with (60% ITU + 15% GI) bonus range on 900 range weapons. You have to get inside their PD range to get the full bonus. Alternatively, you could flip the elite/base effects (and rebalance numbers). Reduced flux cost is much more universally useful, while the bonus damage is only situationally good on certain ships, so it kinda makes sense that the universally useful effect would be the base effect. Maybe slightly buff it to 15% flux reduction, and nerf the damage effect a bit to be in line with other elite effects.
Ninja Edit: I forget the exact mechanism also, but I think have two sources of bonus reduction (range and flux level) really hurts EWM too. Most of the time you don't want to have high flux on the ships that can use EWM because they need capacity to tank damage, so you end up with half or less of the bonus from that, plus the range limit, meaning you are probably getting barely anything out of it most of the time. Especially the AI that loves to hang around max weapon range.
I think elite PD is really cool, but I don't like the base skill much at all. Not really sure how I would buff it though, maybe some buff to frag damage to make those weapons have more utility vs ships or something?
I also think elite missile spec may still need some adjustment, but that might be a symptom of other problems (the amount of extra missile ammo you can get, and the ease that officers can get tier 5 combat skills). Maybe you could split the bonus ammo from elite missile spec (50% base, +50% elite), and then move one of the elite effects to the base skill, or add something else to the base skill. The idea being to make the base skill a little worse for officers, but keep the elite skills strong for the player who will almost certainly make it elite. It would also be cool to see some bonus for missile weapons that use charges instead of ammo, since I think the ROF and ammo bonuses don't really matter much for them.
I'm not 100% sold on the ECM changes. I always though it would be nice to have a total pool of range penalties, and then divide that between the two fleet based on the ratio of ECM points, so if the total range penalty pool is 20% and one side has 50 ECM and the other has 10, then the side with 10 gets 50/(10+50)*20% = 16.6% reduce range and the side with 50 ECM gets 10/(10 + 50)*20 = 3.33% reduced range. That way there is always a benefit to ECM no matter what.
Cybernetic Augmentation changes feel a bit odd to me. In the past, it wasn't strong enough because getting the full benefit required too much of a SP investment, so the solution is to reduce the full benefit? I get that the elite skill buff will make it stronger, but the bonus damage isn't THAT inspiring either, and IDK if it's really tier 5 worthy. But maybe I am underestimating it.
I really like moving neural integrator down a tier, it has a much more clear use case now. Will be interesting to try that combo. I'm curious, does the increased DP from the hull mod count against the automated ships cap?
Hull restorations problem is just all the non-combat skills you have to take to get it. Polarized armor is a bit niche, so if you're not flying a ship that wants that, you're basically taking 3 non-combat skills, just to get it, which makes it clearly much worse than pure combat tier 5s. Might be interesting to try and stack the new DP reductions with support doctrine though, that seems like it could get kinda silly in a fun way.
The support doctrine changes are also pretty interesting. ordnance expertise is a quite strong skill, and I am very interested to see how effective this can be.