I cant say I've expereinced this. Same goes for another vasari issue in another thread. They just dont seem to be happening in my games.
One wonders if by adding 1 unfair player, the AI's all get something unfair added, some sort of bug ? It does seem to be "unfair" behaviour being shown by a 'hard'. I havent played a game yet with an unfair enemy, so that could be why I dont see these sorts of things happening.
My response would be to up my fleet. Choose the battleship with the hardest hitting guns, and build at least 4 more. Then add an extra 20 HC's and another 40 carrriers.
I'm a firm beleiver in dont take 1 when 3 will suffice !

I also dont beleive in fair fights. If you have to fight, have superior numbers or superior firepower, and preferably both ! I'd forget the frigates and concentrate on taking in HCs and carriers, the more of both the better. 50 of each would be a good start. If you have air superiority now, then double it and add in more bombers. I tend to run at a 65/35 fighters to bombers ratio, and while the bombers are not as useful, they do attack more of the cruisers than the fighters do. The fighters swan off and do their own thing while the bombers actually attack something useful.
The secret is in total firepower. If enough damage is done in a single hit to destroy the ship before its restore ability can kick in, then it cant repair itself. So build a fleet big enough to hit any target with destroy levels of fire in a single broadside, and target every ship in the fleet to one ship at a time. And dont target it and leave it until its dead, keep retargetting the same ship every 5 seconds until its dead, otherwise your ships fire once and then seek a more appropriate target for its type.
Target using the icons showing on the left side list, so you can get them easily.
Also, on your own ground, use 4 repairs, not 2.
If all else fails, mod

I upped the guns on all TEC ships, as well as the gauss guns. So I use 15-20 gauss now as defenses, instead of 5 hangers and a few gauss. The firepower on all the capital ships is ludicrous imo, and I set that right very quickly !

The Vasari and Advent have their gizmos, I gave TEC sheer grunt !
Also, if your on their turf and they have a NanoWeapon Jammer, take that out before you do anything else, as while thats running, your hitting potential is zip. You cant kill a ship quickly if your guns wont fire. And while your guns are not firing, repair abilities can maximise their use.