OK..you are describing someone with a maxed out 2K supply fleet. You should have a MASSIVE fleet by then -- maxed out or close to it yourself. If he has superior numbers as Advent AND superior economy, well...you are kind of screwed.
That said, Bobucles is absolutely correct, you need a lot of flak to flat out counter carriers. And the carriers can still jump in and assassinate something, and then run. And Bobucles is again giving you good advice on multiple PJI, hopefully backed by repair bays.
So...at this point, assuming your enemy has commited to this huge carrier fleet backed by Progens + Guardians.....
You make tons of cobalts. You use something like
140 Cobalts w/ anti reactor ability
80 Hoshikos w/ sabotage or whatever it is called (2nd ability)
20 Carriers
50 Flaks
3 Kol
2 Dunov
2 Marza
15 Kodiak
Or some variation on this, as you see fit.
You have to be able to pursue carriers to hurt them. If the other guy keeps double jumping his carriers, they will be at low antimatter. So you pursue them.
You keep your ships in a bunch so your Hoshikos can do their work. If you can handle micro managing splitting fleet elements, make sure you leave groups of Hoshiko's with each element so everything has repair capability, especially your capitals. If it is too much to manage, keep your fleet together ... and just let the Hoshiko's repair as best they can. If you use seperate fleets to manage things, put Hoshiko's in each fleet.
By now your enemy probably has 35 Tactical units of defense in an area smaller than downtown Manhattan and is huddling his ships around it, so if you DO decide to eventually drive up to it, try and make sure a Kol is in front to take the damage. But first, you want him to attack you with strikecraft. You micro the use of your Kols' Flak on your Kols and decimate his fighters when big waves pass over. Suddenly, the remaining fighters are a number that your 50 flak can work with!
You use your carriers to launch fighters against Illuminators. if he has a LOT of Illuminators, you will need more fighters before you transition to Cobalts....if he has tons of Illuminators, you might in fact have to use tons of Kodiaks with lots of carriers to provide fighter cover vs bombers
Now, he might not want to send his fighters against you right away, if he is smart, fearing your Kols. He wants you to charge his strongpoint first. And you will, just as soon as you bomb the living crap out of his planet by driving around the strong point and unleashing your Marza's, and the other caps to assist. Keep ships clustered! By now he is launching fighters and you can use the Kol Flak Burst!
When you approach his mass of Progen's + Guardians + Repair Bays + Carriers, use your Dunov Emp burst... It will wreak havoc with the Advent antimatter and shields. Make sure you cycle them effectively so that when they start to recover the 2nd Dunov burst hits! Then let your cobalts start popping things as they use their anti reactor abilities liberally, as well as the Hoshiko 2nd tier ability. (sorry, forget name)
He will be building Illuminators at this point because he has no direct fire capability. Keep killing them with your Kodiaks and fighters. That is why you have them. Remember to use a Flak burst now and then and keep the Kol out front so whenever things retarget after killing a ship,they immediately lock on the Kol, which is cycling its shield ability. If you have a lvl 6 Dunov, flux field that Kol! Whenever he recolonizes the planet, just kill it again with a Marza. If your fighters are mostly dead, ..heck, even if they aren't, feel free to put Magnetize Hull on one of his Progen's.
You should be pumping replacements into the fight from your side of the lines as fast as you can to replace whatever he is killing....
As his carriers are kind of useless here, he will probably go try to raid you! This is wonderful! If it is just the carriers, you detach the cobalts, flak, and 20-30 Hoshiko's and chase them down, killing them easily as they try to cross your PJI worlds. If it is his whole fleet, you follow...except for one Marza and a full Hoshiko escorts to clean up and recolonization efforts.
Eventually, your Marzas should start hitting level 6, at which point you Barrage his entire defensive zone. He will probably fall back to his next world at some point, maybe with his carriers. You just leave one Marza behind if you have to clean up his colony again, and you immediately chase him to the next world so his carriers can not replenish their antimatter and fully rebuild their strikecraft. Ignore the 20-30 tactical hardpoint of defenses he left. (except PJI! You have to kill those) Just fly around it for awhile. His next worlds are probably not as well defended, and if he keeps falling back, you just keep having your trailing Marza raze em as you pursue and screw up his fleet.
Anyhow, this is just an example of how to fight a fleet with his composition, trying to cover some scenarios. Lots of armor upgrades and lots of Hoshiko's, backed by appropriate counters. If you can't muster a near equivalent size fleet, then your problem is not just fleet composition; it is that he is outplaying you too. Then you have other problems 