Well here's a re-design idea I came up with a while back when I played WoD for a couple months. The stagger idea came from playing a brewmaster tank.
New Passive: 30% of Magic damage taken is staggered and applied as a dot lasting 4 seconds. Still ignores unit collision.
Kassadin gains 1 charge of Force Pulse whenever he staggers 100 magic damage with his passive(this does not need to be all at once, it adds up over time)(max 5 charges)
Q: Shield now lasts 3 seconds(up from 1.5) and gives Kassadin 1 charge of Force Pulse.
E: No longer requires stacks to cast. Mana cost increased to 150 at all ranks(up from 80) and the slow is now only 25-45%
Damage and strength of the Slow is increased by 20% and mana cost of Force Pulse is decreased by 10% for each charge consumed when the ability is cast. (360+1.4AP dmg, 90% slow, 75 mana cost with a full 5 stacks used at rank 5)
R: Range increased to 675. Cooldown increased to 14/10/6 seconds. Grants 1 charge of Force Pulse and decreases cooldown by 50% if Riftwalk deals damage to an enemy champion. Riftwalking onto multiple champions does not grant Kassadin additional charges of Force Pulse.
Explaining my idea:
Ideally these changes would make Kassadin even harder to burst down at the cost of taking more damage overall (loses the flat 15% magic dmg reduction) I hope that it would be smoothed out for Kassadin - especially during early game trades - by giving the shield a longer duration allowing it more time to absorb the damage being applied as the "stagger" DoT.
Removing the charge requirement before Kassadin is able to use his E would give him some more reliable, on-demand damage whenever he needs it. However, spamming it on CD would burn through his mana quickly and would hopefully not be as impactful as his E could be if he saves up 5 charges first.
Having Q grant a charge of Force Pulse is to give Kassadin some access to that strength in his kit even if he faces a pure AD lane opponent/team and having Riftwalk grant a charge...well that's just to make him scary.
tl;dr new passive, longer Q shield duration, E castable whenever but uses charges to reduce mana cost and increase dmg. Ult range and CD up, CD reduced when playing aggressively.