I accept the re-engage as technically valid. Feels kinda exploity honestly. But point taken.
As for the rest. I could argue anything that saves me money allows me to afford better ships therefor combat skill or extra money means restores therefor combat skill for the same reason you listed. Improving your fleet in combat prevents damage, saving supplies, therefor it's a logistics skill. The stretching required to make that connection has the reach to make everything combat or logistics skill.
Everything other then the re-engage is directly logistics.
I'm gonna say that the cost savings from field repairs are large enough when you are taking regular losses that it does begin to enter a realm of its own on the logistics equals combat side of things. It can easily save you 500k-1 million credits after losing a capital ship by keeping one dmod from getting applied, and then later repairing the other one, so you don't need to restore. Especially with story point build ins making just buying a new ship a far less viable method of handling dmods, field repairs gives a very large boost in how many loses you can handle without it being a problem that just isn't equaled by other logistics oriented skills. Sure the dmod fall off takes a bit, but when half the time you don't even get a dmod on the ship in the first place, its just not a big deal. The dmods on my fleet never "build up" despite generally losing a ship or two every major battle, and occasionally losing as many as 7 in one go. Sure, I may have a fight or two with a couple dmods, but they always get back to zero eventually.
As for DC, I think it really ought to be brought back to the "dmods don't impact my combat performance as much and save me operating costs" angle than the "Dmods give me peerless durability" thing its got going on. You could scale back the level of buffs it gives for dmods, but it wouldn't fix one of the bigger fundamental issues I see it as having right now, in that instead of making dmods generally more tolerable, it makes it so that if you want peak combat ability you have to very carefully control what dmods your ships get with reloads so that you get as many as possible on the ship without getting ones that significantly impair combat performance, which is just... bad, and will always be a factor so long as dmods give combat benefits.
For making industry in general more impactful late game, I think giving tier 4 or tier 5s, or possibly both, a bonus to maximum ships in the fleet would be a good way to do it. Industry is supposed to be the "numbers over quality" type tree, and its just never really been able to bear that out once the player starts having a solid income stream and gets their preferred fleet composition. Giving a larger ship cap would really help sell that idea while also indirectly making the tier 4s more valuable, as more ships without officers means more losses and dmods.