I agree with the flaws you stated. What's been kind of killing my love for Advent is also exactly what you mentioned: it seems like Phase Missiles are especially engineered to destroy Advent. This isn't necessarily bad or implausible, but I'd think Advent would engineer something to counter this vulnerability.
I was thinking: Guardians project a shield. If we think of it as an actual shield as in some of the incoming weapons fire collide with it, then it could act as a first line of defense against Phase Missiles also. Fully upgraded, I think a phase missile has a 20% chance of bypassing shields, right? So, any given phase missile fired to the protected unit would have a 20% chance to bypass the guardian's shields, and another 20% chance to bypass the actual ship's shields. This would bring a protected unit's phase missile bypass chance at 4%.
So, maybe modifying the shield projection so that it also adds a bit of phase missile block could be an ok idea?
Another completely different idea here: I read a post of yours some time ago, and I agree with you when you said the main problem is focus fire and how capitals ships cannot hold the front lines after a while. Simply changing modifiers would not do the trick, as there will be always a sufficient force to pop a capital before it does anything worthwhile.
So, I think we can tweak how a capital ship scales with levels. I was thinking: can we make it so that a capital ship will have roughly the same survivability and firepower compared to a fleet at any given point in the game? Let's say a capital ship level 1 is usually found when you have 5 LF and 5 LRM. At this point, a capital ship can dish out lets say 15% of this fleets' damage, and can sustain a minute of focused fire from this fleet. Can we make it so that as our fleets grow and capital ships level up, the scaling is done in such a way where the capital ship will always have 15% firepower of it's fleet and sustain roughly a minute of focus fire from such a fleet? (Numbers up for debate, of course)
So a level 1 capital ship is as it is, then:
Cap ship reaches level 3 around the time where you have 10 LF, 15LRM, 8 flak and 2 carriers. So, the cap ship gained enough HP/armor to still withstand a minute of punishment from all those, and has upgraded weapons which can roughly dish out 15% of their damage.
A level 6 cap ship is around when you have maybe 30LRM, 10 carriers, 15 flak, 10 heavy cruisers. No worries! During the past three levels the cap ship increased enough in survivability to still tank a minute of focused punishment, and can still dish out respectable damage compared to the entire fleet.
Now, I know I didn't take having multiple caps into consideration, but with a scaling like this they would still work if you keep cap ship numbers low. This would discourage getting many cap ships as you want them to level, but would still make them quite powerful and not lose their power at any point in the game.