UPDATE APRIL 2024
Swooping Lunge's +150% melee damage DOES apply to Bladestorm now somehow, and is additive to Steel Charge and Arcane Fury. This is potentially a 2.5x buff to bladestorm if you don't run arcane fury/[Steel Charge], or a 1.44x buff if you run all three!

Bladed [Harmony]'s +25% attack speed DOES work on Bladestorm but the attack speed cap is still at +50%. This means Innodem and Praedos are ideal if you DON'T own Primed Fury, since you can still hit the 50% cap via Quickening/Fury + the incarnon evolutions. Berserker Fury does NOT work on Bladestorm.

Evolution 2 - Striking Swiftness - +30% sprint speed OR Bladed harmony for +25% attack speed if you don't own Primed Fury.
Evolution 3 - Hawk momentum - slide for combo
Evolution 4 - Swooping Lunge - if you can get a kill with Innodem's heavy slash procs while jumping, the +150% melee damage WILL apply to Bladestorm.
Evolution 5 - Armed insipration - 5 combo on ammo pickup

UPDATE JAN 2024
Melee Crescendo can be activated by Bladestorm kills, giving [Ash] permanent x12 combo. You can use this on basically any melee and take advantage of x12 heavy attacks. The best melees for this include [Glaive Prime], [Quassus], most scyhtes ([Hate] incarnon), most two handed nikanas ([Tenet Livia], [Azothane]), most nikanas (nikana prime, sepfahn).

NOTE: I have now turned this build into a general "template" that can be placed on most other non-[Glaive] melees to take advantage of x12 heavy attacks.

UPDATE NOV 2023: The previous broken interaction has been largely nerfed. Some mods seem to still apply but with MUCH lower effect, making it barely impactful.

UPDATE June 2023: CERTAIN MODS and WEAPON BASE DAMAGE seem to apply to Bladestorm and make it deal even more absurd damage now???