Is there a card that turns +X/+X into X +1/+1 counters?
This sounds like a very powerful effect. I wouldn't expect it to be easy to muster.

I could find only two cards that come close:  Vish Kal, Blood Arbiter and 
 Ooze Garden. Of course, these cards are the ones that get bigger permanently, not the attackers. The Ooze Garden is a bit problematic because it requires the creature to survive combat.

You might find an easier way to abuse the Exalted mechanic is to use something like a  Blood-Chin Fanatic. But really, you're overthinking it. The way to make an exalted attacker nearly unstoppable is to ensure it has hexproof and evasion. Hi  Invisible Stalker!