tl;dr: Make monsters slightly resist the specialized (meaning, not Normal) damage they are 'Moderate' against. As such, it would make Acheron's basic attack less effective than Flourish on Beasts.
After some thought, and browsing through the helpful wiki page, I've had this brilliantly dumb idea.
According to this page, a Monster has 3 classes of Defense: Weak, Moderate, and Strong. So this would mean an Undead is Weak to Elemental, Moderate to Piercing and Normal, and Strong against Shadow.
Flavor text from various NPC Knights emphasize expanding your arsenal so you're able to bring the right tool for the right job, and if you don't have the right tool, the next-best thing would be Normal damage instead of Specialized damage. Of course, as the game currently stands, this isn't the case. Under the current mechanics, I could more effectively wipe out a Slime with a Divine Avenger than I could with a Triglav. A Zombie is no match for a Blitz to the face instead of a Pepperbox. And of course, Wolvers are dropping like flies to Shadow weaponry.
Why not add another stage of defense in the middle ground between Moderate, and Strong defense? For example the same Beast from before would be: Weak to Piercing, Moderate to Normal, Resistant to Shadow, and Strong against Elemental. So, suppose a Beast has 65 base defense (going with what the wiki is saying.) This Beast would have 130 Normal Defense, 65 Piercing Defense, greater than 130 Shadow Defense, and a larger sum of Elemental defense. Giving monsters a boost of defense (no matter how small) of the Specialized damage they are currently 'Moderate' against wouldn't affect gameplay too heavily... Or would it?
How about the first swing of Acheron VS the first swing of Final Flourish against Beasts? Yes, it always comes back to 'nerf Acheron' doesn't it?
Acheron does more damage to beasts than Final Flourish or Obsidian Edge on its regular attack because Acheron gets some sort of invisible damage boost for its regular attack because it's charge doesn't have a status.
Fix that first.
But otherwise, this is a good idea. It might completely muck up the damage feedback and make all specialized damage that isn't doing optimal damage, grey. though.