Why not just give him the sion treatment and redesign him from the ground up?
"Blood Mage" doesn't have to mean "His resource is health." Blood mage could mean a of things for his resources. He could have a resource related to blood that wasn't his own health. Every time he used transfusion it could go into a resource bar instead of his own HP, and he could use that to cast his other spells.
Or it could give him a shield and/or extra damage. Or there's no reason why he couldn't use mana.
Just redesign him from the ground up and get rid of the free regen thing. I see him as a bruiser mage. He should be able to stack up and stay in a fight longer. I do like the idea of him amplifying his teams damage, but it's retarded that damage doesn't stick to him and that it's free to heal back up. He needs to have a meaningful cost to healing up. Something other than spamming a low cd q constantly. He should be able to stick in a fight, but damage needs to stick to him, or he absolutely needs needs to revolve around sustaining himself he shouldn't be able to burst heal himself up to full health after every trade. Especially when he gets so strong late game.