I am working on using the mod more, though it puzzles me a few times.
Part of it is the delay to see changes. From what I understand it civilian buildings takes priority over military station for cargo-ships, so Militia Heartquarters can take several minutes or more before a cargo ship arrives to start production. I think each heartquarter produces different ships for military like civilian, but it might be by planet for military.
I noticed pretty much all trade stations are maxed out at 24XX/2500 on their resources, even in a completely secure environnement. It might make the battlestations trade post sort of redundants. Though, there are less cargo ships everywhere which used to be a sort of problem. I do like the new mini-cargo ships, it's cute and make the planet less visually busy.
The ship caps on the heartquarter kind of confuses me. I think the cap increase when you have more of a resource available(ie, more trade post of that resources). Though with cargo ships having difficulties bringing the goods sometimes, it led to me building 4 trade posts on a planet 5 hops away from the homeworld, with the heartquarter on the homeworld at 0/324 sniper for over 30min so far (though it might have built a few at some point?). Anyway, I think the more trade post boosting ship cap is what is happening but I am unsure if there are others factors.
I am still experimenting so I haven't gone far with the military various boosters to boolster cap. As far as I can tell, I need to build wide initially to get more planets boosting more caps and allowing the civilian patrols of each planet to reinforce their neighbors at need. Then when I get enough energy, I should build tall in a cluster with 2-3 battlestation to get crazy-high cap everywhere and use that both for defense and overwhelming defense. We'll see.
Logistical Station on pretty much every planet seems to be a given with Civilian Industry. It allows the cargo ships to move faster as well as the patrols, gives me the best defensive options against raid, while pumping enough energy to get by. Also because science needs to go wide since the first two tech levels are a significant boost to all civilian forces, I need all kinds of tech, meaning investing in a single type of station is the superior option. A focus on light hull might be better too, since it upgrades cargo ships though I don't know if it just makes them tougher or also boost their cargo size.
In term of offensive use, I use the the battlestations forces as reinforcement, with my main fleets taking the brunt of the damage and initial attack when invading a planet. It's easier to refill the main fleets but the civilian battlestation-fleet can adds significant firepower when clearing a world. It certainly helps that in my last game I got a focus on long-range civilian with Steel giving me Concussion ships.
Performance wise, things seems a lot better than they use to be. I am playing a 200 hundred planets game to test it so we'll see how that evolves.
Edit: After focusing on a save where I slowly went from one to four planet I seem to get where the problem lies with Cargo being "slow" to get resources around. It looks like they spend a lot, like a lot, of time loading/unloading trade posts in order to get 100/100 of each resource loaded before going to a military post/base/Etc...
So, they "unload" at a trade post lacking a specific kind of good, then load up... except that in some case in the process of "loading up" they go to another trade post because "it's lacking in X and Y resources" among 3-5 different resources. But then the trade post where they loaded up is empty again... so they start taking out resources from the post they just refilled and go back to "solve" the shortage on the earlier one. A vicious cycle.
If you cheese RNG to have only a single type of resources (or use just the homeworld early on) the cargo ships perform incredibly well.