I’m glad to hear that your vital resources are underwater, I think it suits your concepts. (Lest you think I’m slow, it is perfectly possible to have a water world where everything important floats on the surface, and until now you hadn’t said anything that ruled out the possibility in my mind).
“Fighting with a huge distance between” is smart until your opponent puts a ship in orbit. Then you’re boned. Or if they have missile subs. Then you’re boned too. (There are feasible antimissile defenses from low-index up, but they’re not even close to perfect, so you are still at risk from missile subs, while they’re not at much risk from you until they choose to open the engagement).
High index tech can provide defenses, but you run into another problem there: If the tech is small, why not mount it on a heavy a-grav sled? They’re faster and more versatile. If the tech is big and expensive, why put it on an immobile surface-bound hull instead of reserving it for more-versatile, more-useful, higher-prestige Hammer keels?
Iron Empires a-grav is relatively versatile. You’re right that it doesn’t extend to battleship weight classes (well, it does, that’s how spaceships land, but it doesn’t have combat maneuverability in that application), but it’s not just for fighters and speeder bikes either. A-grav tanks are common and awesome. It’s fusion-powered, so you don’t need to refuel or anything. You may still need some kind of tender, but it would be a strictly non-combat vessel, more akin to a land-based airfield in its battlefield role.
Of course, you could always rule out a-grav (either the world’s just lost the tech base to manufacture it, or maybe there’s a silly planetary anomaly, or just really really effective grav-seeking missiles) and then you’d need carriers again.