I know you said no theory craft, but oh well... I'm not presenting this as fact. This is sheer theory, but I'm thinking this would work...
For the Vasari (because I hate playing as TEC): Skirantra+Kortul.
Skirantra: This ship should be held back and should have its SC set to all fighters and be guarding it and the Kortul. Ignore SB and go straight for Repair Cloud. For your secondary, get MPA. Your fighters need all the survivability they can get. The point of this ship is to kill off their bombers that they send at you and if nothing else neutralize fighters.
Kortul: This ship should be up close and personal with the enemy ships. You need DS to knock down their AM levels so that you can stop telekinetic push. But the primary ability should be Jam Weapons. You need to neutralize their fighters and bombers as much as you can. Neutralize their SC presence and their main advantage goes away.
At the beginning of the battle, send your Assailants and Kortul to the front lines to blast away at any Disciples and have the Kortul target the Halcyons directly to wipe out their AM. The Skirantra should be in the rear and hopefully aided by a repair platform or two (and maybe some missile platforms as well) You want to be on the defensive when you do fight this battle. You need that advantage.
As the fight drags on, keep your capital ships alive at all costs. You need those abilities up. If they go down, you die. Plain and simple. Also, any hangars you can get up to boost your SC numbers are going to be huge helps against ADA. Eventually, you will drain his AM. This will result in no more TP slaughtering your SC. Without this, your Skirantra with its RC and MPA ought to give you an advantage, even if only slight. This gives you the opportunity you need to kill his SC.
Once he has no more SC, you have the advantage as those Halos are sitting ducks for your Assailant army. Yes, he will bring scouts, but your fighters (now that they have killed his SC) will have new targets. Once he retreats, repair your forces immediately..
Also, if he brings out counters to your LRF's, get more hangars and repair platforms up. Also, missile platforms are equivalent to about two Assailants, and scouts don't counter them. So keep that in mind as well. Also, get phasic trap up as soon as you can. Between that and Jam weapons, his SC should be sitting ducks for your flak and fighters.
If he brings in Illuminators, get feed. He is being fed, so you need that extra boost. Get an Orky if possible, but make sure that it is within range of RC and your platforms when you do. Once the Orky is upgraded, your victory is almost assured. Highly upgraded Orkies are things of might. They can also tank enourmous damage and since Halos don't really deal that much themselves and a single volley of PM's from an Orky deals 325 damage (let alone what happens if multiple banks fire at the target which results in more as the 325 is per bank, and it launches PM's from all four banks).
In other words, if he brings counters, you bring counters. If he get's fed, you need to be fed.
Once again, this is only a theory, but I figured I'd post it so that if someone wanted to they could test it out. I personally don't know, but it is logical, so a test to see how close it is and whether it needs some adaptations, should be abandoned, or does work.