He is not a vampire, he is a hemomancer, a blood mage. You should cast one glance at any usual vampire weakneses and then throw the whole lot out the window because despite how much he may reference vampire mythology in his skins and such, he is at the heart of his lore not a vampire.
Any changes made to him should reflect this. Keep the vampire references for the skins, especially since there really is very little vampire in his fighting style. Most vampires just drain blood, they dont use it as a means of attack.
Now what should be done?
I feel he has to keep his drain style in some way, he is a hemomancer who invogorates himself by taking other peoples blood, you just cant get around that. But perhaps the drain focus can be changed, that instead of healing off healing he drains other things? His lore, old and outdated as it may be, references him absorbing his masters talents through his blood, so what if instead of healing off some of his attack he started draining stats? A whole new can of worms perhaps, but just a thought.
Some of his healing has to go either way, it is the core of his problem. He is either fed and oppresive, able to outsustain anything thrown at him or pitifully weak and useless as his healing cant keep up with his enemies. As long as this exists, Vladimir will be a nightmare to balance.
Maybe a limiting factor could be that enemies struck by his attacks leave pools or even trails of blood ala Nocturne's Q or Zac's blobs and he has to actively be on those trails or in those blobs to heal, possibly making his pool ability also collect any trails or blobs in an area around him? Change it up to be a mage who needs to be in the thick of things, much as now to do the bulk of his damage, but emphasize that he needs to move around to stay healing as he absorbs the blood of his enemies?
Just throwing ideas around here.
Also unrelated, once his rework is complete, give him an Ionian inspired water style skin ala the Waterbenders of Avatar: The Last Airbender, as a reference to bloodbending. Just a thought.