So you'd counter balance with balance?  Then just win with better skill or something?  I'd rather win with unit composition, LOL.

I guess the ideal counter to mixed flak/lrm is hc, but for this hypothetical let's assume this is unavailable, impractical to attain, whatever.  So hc is out.  What would you counter with?  In theory you could say "I'll counter his lrm with scouts or fighters, and I'll counter his flak with lf," but then his lrm will murder your lf, and his flak will murder your scouts/fighters.  That's why I said "all flak or all lrm."

So what fleet would you use against this fleet?

Early on, scout/LF will actually work.  Scouts can kill the enemy LRF fairly quickly, which then leaves only flaks that your light frigates can clean up.  With the right capital ship on the field, you can get a lot of momentum early on. This is particularly useful for Advent, but won't work as well for Vasari due to their weak LF and scout.  Support cruisers, particularly the hoshiko are great choices to back up your army since LRF and flaks generally don't kill them easily.

Carriers are a great selection.  Even if flaks are on the field, with the right kiting and maneuvering you can whittle down enemy LRF numbers.  However, this is definitely a more micromanagement-based army so if you want to win with pure army composition this isn't the path to follow.

The best counter to LRF/flak (repulse notwithstanding) are heavies, preferably backed up by support cruisers.  Unfortunately, it's entirely possible for Advent illuminators to brute force their way through enforcers with sufficient numbers, so Vasari is kinda in trouble, but in every other matchup heavies will do the job.  As you mentioned, they're also high in the tech tree and probably not viable.

Unfortunately, beating LRF/flak by army composition alone is very difficult.  It simply offers the best performance for your money, and between those two units almost every unit type in the game is countered.  You can counter it early-game quite nicely with scout/LF but that doesn't scale very well later on and a smart enemy will bring out his own counters anyways.  You can try carrier-spamming with bombers, but again a smart enemy will bring out his own counters.

Scout vs LRF isn't low DPS, and once the LRF are dealt with the enemy is also low DPS.  If the enemy can kill your scouts before you can kill their LRF, then you have problems.

Yes, that is the second weakness; capital ships fare much better against scout/LF then they do against LRF/flak.  However, it's all about picking the right caps and abilities.

If there are other units on the field, the smart player will ignore the cap and attack its support.  If it's just the capital ship, then even these units will take it down and force it to retreat.  The real danger here is of course the carriers caps, but it should also be noted that they threaten LRF-based strategies just as harshly early on.

Remember that flaks won't keep carrier caps under control, because carrier caps require no antimatter to replace their strike craft.

Try an Akkan with ion bolt.  Carrier caps are the most fragile of all capital ships, usually relying on kiting to stay alive.  I've killed more than a few carrier-first capital players by using Akkan or Jerrasul (gravity bomb) to cut off their escape while my "weaker" units kill them off.

well assuming that's an option, of course i would do that every time (and if 10 to 1 is an option, i would do that).  but this question is based on the assumption that both players have roughly equal resources and positions and fleet supply.  this is a question purely of "what is the best combo of units to build to counter X?"

The problem with going pure hoshiko/flak is that this just invites Advent disciple spam, which (now that LF have been buffed) is pretty dangerous.