I could see the Life Boat still being included, to reflect emergency rations/escape room in case the Small Craft has a problem. If the Small Craft loses primary life support, the Life Boat is a separate and contained life support environment that can keep a 6-person crew alive for the next two weeks.
I'd still want to increase the Miryu's mass so it could carry enough fuel to go from the Jump Point to the planet and back on internal fuel. Each of your Docking Collars can handle Dropships up to 100 ktons in mass, I'd recommend increasing the Miryu's mass to take advantage of some of that capacity. I don't think you can use a pair of Small Craft Bays to store a single 400-ton Miryu.
Did a cost study on the Centrella by increasing its mass to 700 ktons while keeping all else the same. This raises the cost from ~9.1 billion to ~10.7 billion, and allows for an additional ~100 ktons cargo room.
This might be a future idea to hide larger hulls under the same design specifications (fuel capacity, weapons loadout, armor tonnage, etc), but have plenty of room for future expansion. In the meantime this larger design can serve as flagship or critical materials transport.
The later upgrades would involve moving around the Naval Lasers to make room for an additional 22 HNPPC, for a cost of less than half a billion more. The doubled hull size would also allow adding another 490 tons of armor for another 49 million in cost, almost doubling the protection. It will wind up needing 41 officers and 259 crew, leaving only enough room for 15 passengers.
That extra cargo space might actually be important and/or useful, particularly for the flagship role, since it lets you carry enough schleppage to refuel other units in its group, carry spare ammunition, spare parts...
Main thing I'm seeing thus far in this challenge, is everyone's doing combat units, nobody's doing the things that actually make your Navy a Navy instead of a collection of expensive collectibles.
Particularly given the state of things at the start of this as posited by the OP.
What is actually
needed?
1. The navy needs the ability to support itself on deployment. This is first-and-foremost, given the lack of shipyard spaces and their concentration in vulnerable locations especially. Flag vessels need to be able to support the non-flag vessels, because for a lot of the time, they're not going to be lingering next to a shipyard location where repairs and restocking can be done.
2. Fuel, Charging and Communications links, logistics vessels, etc. etc. etc-your patrol radius is decided by how quickly fuel and spare parts can arrive, or by how long you can run on what you're carrying. I was kind of tongue-in-cheek on the Miru's lack of fuel, but it's a serious problem for anything that
isn't an immediate local defense unit. The fuel on a Warship is also the fuel they feed their fighters, small craft, or escort dropships. Supplies carried as cargo aren't just there for THAT ship, they're there for the lesser units in that ship's escort group, including fighters and small craft, and assault dropships.
In the immediate situation, I see a few different approaches, but the one I'd suggest, is bulking up your production of things like portable yard facilities, charging stations, and supply jumpships first, with medium weight duration ships that may not have "AAAALLLL THE FIREPOWER!!!!" but can definitely stay in motion, and keep their support elements in motion as well.
Basically, I'd invest in Trackers and supply/logistics stations with assault dropships as supplementary, and only after I've got decent amounts of coverage within my domestic borders, put some investment into building bigger ships, probably starting with 'Destroyer Leaders' and finishing on a medium weight Cruiser design that can be made cheaper than the ornate battleships the neighbors plowed their tax funds into.
but then, I look at it a bit like an economist-a navy you can't keep manned, fueled and fed, is a navy you can't use, likewise for a navy that can't absorb losses, because no matter HOW big you build it, no warship is invulnerable. If I lose a Tracker damaging the hell out of a Leviathan III, then that Levi has to retire to get repaired, and it'll cost as much as TWO trackers, that can cover more systems more efficiently, across a broader set of requirements than "Flagship for an invasion of a planet".
Second thing, is 'Fleet in being'. This forces your opponent to counter you, even if you shy away from direct confrontation-he's got to account for your fleet striking somewhere he's vulnerable while his ubar warship is striking at a single system.
(I actually demonstrated this in the FC'62 game by breaking up ordinary jumpship groups and scattering them around-it stopped the massive all-Leviathans-invasion-fleets of another player and forced him to move through unclaimed space one hex at a time...to deal with a single ship. This has been shown to work with real life forces in the past-if they know theres someone lurking in the back field, they tend to move slower.)
Third is consolidation. This is why communications is so important. The hypothetical Lone Leviathan can be caught out by arriving task forces and he has to face multiple opponents, possibly from multiple directions, simultaneously (or near enough).
Or, those ships can be busy flattening his logistical tail, striking his industrial base, and kllling everything he doesn't have the Ubar-Warship to defend.
Point being, in a single engagement, bigger might be better, but smaller is more likely to win actual
wars.