One possible solution (as already proposed) would be to add a "third" version, "Normal Mode" and simply double the drops in Savage.
So we'd have the following layout:
Story Mode: 190 gear (tokens), basic mechanics.
Normal Mode (Roughly Coil Difficulty): 210 gear (2 items), new mechanics, slightly higher boss hp/damage output, MAYBE a bonus boss or new phase in every fight to add an experience or minor lore incentive, without affecting the outcomes from Story Mode.
Savage Mode (Current Savage Difficulty): 210 gear (4 items), no new mechanics from Normal Mode, just tighter dps and healing checks.
The idea is that you do Story Mode for the overall story and to see the fights.
Then you have Normal Mode which is for the "mid-core" raider, which is most of the raiding community, where you get better gear, new mechanics, and a new phase or boss form change in each fight, like having an actual "Boss" on Floor 2, or having the Manipulator with reduced HP, but when you beat it, the "Pilot" comes out as a second phase, creating a whole new fight.
Your reward for completing Normal Mode lore wise, would be additional exposition, adding some interesting details to flesh out the story, without having any real effect on the outcomes of Story Mode.
And finally we'd have Savage Mode, for the real hardcore raiders who want it to HURT.
Same mechanics as Normal, same extra phases/sub-bosses, just tighter dps and healing checks to REALLY make the most of your gear and skill... Basically this would be the "how long can we stump Lucrezia" version.
The reward for beating Savage is that you get 2x, if not 3x as many drops per Floor, as a reward for overcoming the challenge. Of course Normal Mode and Savage Mode would share a lockout, to force people to make a conscious choice about whether they want 2 drops from Normal, of try their luck in Savage for 4, maybe 6 drops. - There's your hardcore raider incentive.