About the fleet admiral thing...
Not terribly seeing the point of the Admiral ship in that sense, really. If you think about it, a truly epic game shouldn't end up resolving around a single powerful ship - it's far more satisfying to watch squads of capitals with fleets of support craft venture forth and Lay Down The Smackdown - the US had more than one battleship in WWII, afterall, and that's always been the sense of 'capital ship' that Sins gave me, rather than having a Hero Unit.
What I'd much rather is a way to designate a fleet admiral, and have them grant abilities to their allies. If it was level-based, this would be a nifty bonus.
About the fleet admiral approach.
I believe it's a different idea, and is not incompatible at all with the Grand Capital Ship idea. Let me explore it.
I am supposing it's possible to use a structure with a skill which can 'buff' a cap ship with a permanent bonus. It could only be activated by research a high level research. I believe it makes no sense to buff a smallish fleet and give nothing to another fleet in the same gravwell if there is an Admiral commanding the action. therefore, the area of effect of an admiral should be the entire gravity well the capital ship is in.
The skill needs a high level research, a high level cap ship (6 or higher), and a tactical structure (Strategic HQ). It works like a passive skill bonus. For each Strategic HQ (info about its resorce cost later) you will be able to buff a single capital ship, which will have this bonus until it is destroyed.
The upgrades would be paid for on the Strategic HQ, but the bonuses will take effect on the 'buffed' ship - the buff IS the Admiral.
The admiral would give a base set of bonuses - like +5% everything - range, speed, cooldown, shield/hull/antimatter regeneration.
We will then be able to pick and choose the extra bonuses the Admiral is able to give. Like the starbase, you have more options than levels available, so you must pick and choose the ones you want. If the ship with the Admiral dies, it will take some time (3-15 minutes) for a new Admiral to be available.
As for limiting the number of strategic HQs, There are a few possibilities I can think of:
1) It is a structure with a huge tactical slot cost, enough to guarantee that no more than 1 can be built on a planet. Probably expensive enough to guarantee that an asteroid (2 tactical slot upgrades) can never host one.The tactical capacity will be crippled, so it is a tradeoff and must be protected accordingly.
2) Or it can be a starbase. So you place it, but it has only the 'basic' level of defenses. The upgrades go all to the Admiral. It is a reasonably strong defense asset, but no nearly as strong as a fully upgraded SB. That makes it a more vulnerable target, which needs to be protected.
3) Stars can have up to 4 starbases. If the number of 'starbase slots' a starbase uses can be altered, so that a 'super starbase' can be designed, we can make a starbase which can only be placed on a system star, taking up 2, 3 or 4 starbase slots. That ensures that very rarely more than one admiral will ever be present (per race) in any game. In this case, since the Strategic HQ is such an important asset, it should have strong defenses by default, like a level 6 starbase probably (2 offensive - 2 defensive - 2 strike craft upgrades) at its base level. It will be alone in the star, with no tactical structures available to help it. Maybe it could take 3 starbase slots to allow for one additional starbase companion to help it fend off enemies. I would make it cost a LOT, start strong, take a very long time to finish constructing, and be a 'no-weakness' fortification. Which means, weapons with range long enough to take out Ogrovs. It is a Strategic HQ after all. Only sheer military might could bring it down.
I would also make it take a percentile of the Empire's income, much like the fleet size does. It should take a huge amount of resources to make the Intelligence running, So I would give a 3-10% percent economy impact.