Or, the grand simple solution is to just put the TEC's LRM technology at a higher level(Tier 3 or 4). This means that you get counters(carriers & flaks) on earlier levels or on the same level. Of course, TEC missile technology requires the Javelis to be unlocked, but that problem can be fixed by just removing the prereq.
Presently, LRMs are Tier 2 tech. Flaks are also Tier 2, but they're too much of a niche product that are useless against anything except LRMs and strikecraft, and LRMs can just fly through/around them anyway. Carriers with fighters are Tier 3 for the TEC and Vasari, and even though they are Tier 2 for the Advent, LRMs are simply too fast for a kite-attack to be feasible without a meatshield - and meatshields are Tier 5 technologies(Heavy Cruisers and Repulsion). Scouts do do some considerable damage to LRMs, but they get killed easily and take longer to build en masse(for an equal fleet supply) even if they don't cost more resources.
Level 6 abilities like Cleansing Brilliance and Volatile Nanites crush LRMs, but they are after all Level 6 ultimate abilities, and your battleship would end up dead against LRM spam before it can get that much XP.
We see the same philosophy in Supreme Commander, where "Tier 1" defenses are extremely effective against early rushes, and defenses powerful in the early and midgames, but fall easily to highly effective lategame units like siegebots and experimental units.
This philosophy is implemented in GalCiv 2 as well. Starbase fortifications are amazingly effective against early-game corvette fleets, they gradually get weaker as larger ships come along, and once you have fleets of Huge-hulled dreadnoughts running around with Doom Rays and Blackhole Eruptors, Starbase defenses become useless.
But here, defense turrets can't even shoot at LRMs and hangars get killed by them rather quickly.