I'm going to begin with the caveat that I only have time to play single player, so my thoughts on this matter may not be as relevant as some others'.  However, from what I know of the game, my input is as valid as I say it is (and by no means do I maintain that it is without error).

Scouts are, as you've discovered, just too weak.

Trying basic assaults was...attack wise, a better idea for the money than scouts.  Defense wise, though, it was suicide-you're doing 75% damage and taking 150% damage.  (I seem to remember the Illuminators having a non-standard damage type for LRFs, actually, but let's just go with 150% for now.)

Carriers full of fighters wasn't a bad idea, but as you say, they're somewhat more expensive.

Your two remaining options would seem to be LRMs and Kodiaks-but Kodiaks aren't exactly early game.

Javelis outranges Illuminator, and Javelis is frontal gun only, while the Illuminator is split between front and sides.  Based on the LRFs' max speed of 500, you'd have ~6.5-8 seconds of firing on the Illums before they got in range of your LRMs, and LRMs are damage and supply equivalent on a cost basis (roughly).

For the purpose you're intending to use it for (fighting Illums), this would still be underpowered.

Running the raw numbers (which doesn't necessarily account for everything), increasing the scout's firepower by 23.5% to 26% (factoring armor in as hull or factoring armor in as hull/shields) puts it on a roughly equal footing with the basic assault when factoring in ship cost, ship hull/shields/armor, and damage types, in terms of damage done per survival rate per cost.  That is, if you spend ~79-81% of the amount you spend on basic assaults on scouts instead, you'll do the same amount of damage to the enemy illums in terms of fleets.

Do keep in mind that for the sake of keeping things simple (haha, yeah right) I purposely neglected to factor in the 55 metal cost per Cobalt; particularly as I don't tend to agree with what appears to be the rest of the community on what the credit conversion factor would be-so the point where the Cobalts and the Arcovas are equivalent will be closer than I've estimated.

But the point remains that basic assaults, with their 75% damage modifier to LRFs and 150% damage modifier from LRFs, were obviously not designed for that purpose, and scouts are hard pressed to beat even them at it.

So I'd say anything less than a ~70-75% increase in firepower would be insufficient for your needs, and that's...probably not going to happen.

Conclusion: Try Javelis and report back.

I'm not aware of any "pros" claiming that TEC is inferior to the other factions.  I have heard a pro say that TEC was vulnerable in the opening phase of the game if a vasari player were very close to him and rushed him, but that doesn't seem to be your problem.

Try scouts again, but build a TON of them - I mean a TON.  If he composes his fleet of all illums, you should win.  If he has other things mixed in, well, it's more complicated, and scouts alone may not work.  Beef up the scouts too - as much armor, hull, shields, and weapons upgrades as you can.

Secondly, one guy here suggested rushing him.  He's teching to illuminators, and that's 3 military labs.  You can get lrf's in 2.  Heck try a cobalt rush which doesn't require any labs.

Fighters are a good counter, but you will have to build the appropriate numbers of carriers, and micro them.  I know you said they are expensive, but his illums are too, aren't they?

If nothing else, lrf's should put you on par with his illums (built in appropriate numbers, of course).

Finally, your flak frigs should do decent damage against light armor, plus they are cheap, and tough as hell (heavy armor).  Try building as big a swarm of those as you can, and drive them right into the illums.

Match his illum fleetcap with your counters.  If you can afford to, exceed it.