Well i agree with mostly you said, except for autocannons. They might be good for fortress but so they are plasma cannons. They should be useful for normal fleet combat too. If that means tweaking them, ok for me.
Not that stations are good anyway, they usually are a minor annoyance and very costly to build and maintain. Autocannons right now are useless imo. they do not act as PD as you previously said (i tested them several times), they have horrible range and horrible accuracy offset by the high rate of fire. But before the fleets engage any other weapon system will deliver more damage (and also killing blows so the returning fire will be even lower) that autocannons will once the fleets engage, because the damage difference is not that huge. They also cost like a railgun or laser in both energy and minerals. I sincerely think something needs to be done with them, either in costs, damage or range.
I suggest to up the range a bit to be usable like 10-15-20, lower the energy consumption, buff the accuracy and lower the damage per second, while maintaining the rate of fire. They could act as a good low range option for small ships that engage close and personal other small ships and they could act as a defense weapon for big ships unable to hit small ships with the other guns.
Maybe lower the lasers and railguns 10% the accuracy to fit in the autocannons? so standard guns get 80% hitchance and autocannons 90%. then lose 2,5% for each size. it ends at 80-77,5-75 for standard guns and 90-87,5-85 for autocannons.
The problem also is that hit chance is hard capped at 100%, so right now with the new marksman computer you added and the other configurations, hit chance is capped easily. Maybe that is what makes you think autocannons are really good, every gun ends with 100% hit rate with one or two upgrades. That could be the reason AI loves plasma guns so much too.
Navigators guild bonus (10%) + computer bonus (10/20%) + fleet academy (5%)+ tachyon sensor (+10%) means that you get 35-45+ (!) bonus of hit chance. I think that is a major point to touch next.You could add 2% for navigators, 2% for academy, 5% for tachyon (1/3/5), 3/6 for computer and you could end with 15% max of increase hit chance. a Large standard weapon end with 90% hit chance. Extra big guns like kinetic batteries or lances could be 80% accuracy, so they are good as a long range gun but can miss, even with all the bonuses.
Now if we do the calculations, the autocannon dps could be set to 15% less than standard guns, but the extra 10% accuracy is a world of difference in the additive game of evasion. It could end at 20% more effective damage vs evasive ships but lower damage vs non evasive ships (they dont evade, then the lower dps show up). Corvettes now dont hit 91% evasion anymore, but maybe they can hit ~50% (50% currently, 57% if you set thrusters like i suggested to 10-15-20-25). Lets say a corvette hit 50% evasion vs full upgraded ship wth sensors, computers and autocannons, you are hitting 50-47,5-45% of the times. With a railgun you are hitting 40-37.5-35% of the times. That is a huge enough difference to set a spot for those guns but not enough to break the game.
If you dont want autocannons to be anti small ship guns, you could also change the large mount to do more dps, like a lance or kinetic artillery and set it to 10-15-15 range. Large mount gets same range of medium mount, but instead being designed for shooting small craft, it gets lower accuracy and a buff to damage and rips big ships apart.
The ships stuck might be about the bug of formations. there is some huge issue with formations and range, it seems the formation range overwrites weapon range. There is a mod, rangefinders or something like that it the workshop that fixes that somewhat by forcing a set range that the ship will try to maintain. That could be a temporary fix.
There is also another problem, there is a modifier to combat speed set for each class and maybe the big ship ones is too restrictive.