Holy shit are we seriously playing the same champion here?
Vladimir's main issue right now is that he's too safe compared to his dominance mid-game to falling off in the late-game, due to his awkward mixture of decent tankiness, decent damage, and no utility. Safety in the early game is one of the last things Vladimir needs right now; currently he can win most of the popular top lane matchups.
That being said, I wouldn't touch his W cooldown. Since most Vladimirs would leave it at level 1, out of necessity more than anything else, being increased in the early levels would even further Vladimir's feast-or-famine playstyle, since it screws him over insanely once behind. (And maxing E last would only make him even more useless in teamfights, so it is not an option.)
Anyway, I think giving an AoE slow onto his R offers too much power, and it will have to take some from somewhere else... meaning even less damage and that's problematic in itself, because that would make Vladimir just a worse subset of other champions. I would instead grant something similar to Darius's passive, so +5% MS for each champion hit for the same duration as the debuff, this would help solve his mobility issues in teamfights- which would be great as Vladimir's range is a huge limiting factor in Vladimir's late-game. And remove that bullshit post-action delay, of course.
EDIT: Realizing I haven't contributed much of my own, here are my ideas:
*Gut Q's healing and instead give spellvamp onto E stacks (-5/level and -0.15% AP to Q, +4% spellvamp/stack on E). One of the major factor's to Vladimir's feast-or-famine playstyle is because how safely he can freeze lane and then poke with his Q when he goes ahead... and can't when behind. Q is especially troublesome because it is an instant, targeted ability with no opportunity cost. Compare this to E for example, which has the drawbacks of pushing the lane. I chose to nerf healing than damage, because it'd be hard to balance the damage without making it useless, and the healing allows Vladimir to be brought down by repeated engages or through heavy poke.
*MS boost for each champion hit with R (e.g. +5% for each champion hit), for reasons listed above. This helps solve Vladimir's range issues late-game. That and remove the post-action delay.
*Reduce E's base damage slightly (e.g. +10 at level 1 and -5/level for -30 at level 5/full stacks), to increase its scaling (e.g. +0.1% AP), and increase the AP->Health scaling on Crimson Pact (e.g. +0.4% AP). This will help flatten Vladimir's power curve into the late-game, which is desperately needed because Vladimir is huge mid-game... but is sorely dependent on his team to turn it into anything useful. A mid-game power spike with no range or utility is just absolutely horrible as a concept.