1. Be aggressive early on with LRM to not allow mass Illums.
2. Strike craft hit'n'run (you didn't mention Defense Vessels anywhere). Fighters will tear through the Illuminators.
3. A well-balanced fleet with Kodiacs, Flak Frigates and Javalin LRM with splash upgrade. LRM can stay back, Kodiaks take the beating while the Mothership eats the missiles. After it is down, Kodiacs and LRM will make spacedust out of massed Illuminators.

But it is true, Malice is an incredibly powerful spell.

in adition to the lrms, send in some groups of about 7 or 8 krosov seige frigates, this, as it stands now, can normally kill a planet with lower defenses or wil only a small defending fleet
an early attack by seige frigates, if sent to areas far apart in their empire will keep you and your fleet occupied and split up so you dont lose planets, by the way, this is a strategy the AI seems to like... and it works quite well seige frigates are fast and in numbers do tons of dmg to planets


for countering your fleet, i would suggest the strategy i have adopted for most game, which is build almost 100% capitol ship fleets
by the time you have the above mentioned fleet, they could easily have 8 capship which if firepower was concentrated on one of yours, would be devastating
the key to winning battles against most fleets ive found is to concentrate ALL firepower on the enemy capships, cus noone likes having their frigs w/o capship support as they just get chewed up by enemy capships, and thus AI and even players usually flee... players often flee even earlier than AI to avoid what will obviously be a capship loss

Javelin LRM range is a lot bigger then the Illuminators If he wants to fly to the LRM to kill these he will stand right next to the Kodiacs with his Illuminators. Kodiaks deal wonderful damage to Illums so they die fast. In addition to that, the side beams will fire at the Kodiacs and only the front beam will kill Javelins - so the Kodiacs can tank reasonably well. And either the Kodiacs or the Javelins can have Malice on them since they are positioned so far apart - not the whole fleet will take damage.

The Dunovs abilities are perfect for anti-Advent. EMP Burst brings down enemy shields and antimatter to an extent and Magnetize temporarily makes the target ship attract strikecraft and collide with it - great for a 1-2 punch against the 3 things Advent focuses on: antimatter, shields, and paper-plane strikecraft.

TEC players can mimic your early strategy as well, and get a Kol as the 2nd capital, which pretty much destroys things easily.

Then TEC players can really pump out a great economy and pretty much bury you with some of the larger fleets they can get in late game. A fleet early on consisting of frigates, LRM and a Kol can mount a formidable offense/defense while they have a 2nd fleet of the Akkan and some frigates/LRMs colonze planets rapidly.

The only problem is early in the game TEC has slow fleet building until you get trade ports up and running. But once trade ports are up TEC can build very very rapidly.

Flaks pwn Illuminators.
Capital ships? Quite frankly I never go past one. The prevalence of LRM, Bomber and Heavy Crusier is so strong in this game that they really aren't worth building

Yeah that personally makes me kinda annoyed. It is so easy to just focus fire capital ships with massed heavy cruisers and watch them dissapear, its not even worth the cash. Grab an Akkan for the limited time it'll give you the targeting link and a dunov to do that initial EMP burst and wave goodbye...

LRM, Bombers & Heavy Cruisers only deal 75% damage to Capital Ships.
And if you have problems keeping your Cap Ships alive, then you need to invest a little bit more into support cruisers.

But yeah, otherwise, Illuminators are quite trash, definitely not worth it without the Illusion upgrade.
Why would a ship with Anti-Capital weapons place their weapon so they must spread their damage over 3 different targets?
Crazy.

That strategy is exactly why they failed to beat you.

First, they focused their fire on the capital ship. A capital ship is quite tough, and focus fire has diminished returns. In other words, they wasted a lot of firepower just to attack a capital ship. Capital ships aren't threatening enough to waste an entire fleet of firepower.

Your strategy is easily beaten as well... it's just that your opponents don't know it. Fighters (carriers have 'em) and the flak frigate will do some heavy damage to your fleet. My strategy would be a mixed fleet consisting of some repair ships, a lot of carriers, some a bunch of flak frigates, and a bunch of LRM ships.
Basically the combat strategy looks like this:
Carrier w/ fighter > Illuminator
Carrier w/ bomber > capital ship
Flak frigate > Illuminator
LRM > standard frigate
The capital ship doesn't matter to me... they can use whatever they want to use. I'd go with the carrier cap ship or the combat cap ship.