Uh, what is the difference between the regular and upgraded versions? Unless I'm tripping out, they're exactly the same right now.
Also, Necromancy tends to hint at resurrecting rather than healing. On that note, how would "Soul Drain" or "Soul Orb" fare? For the latter, I was thinking of an orb to act as a sort of storage vessel for the absorbed souls that fuel the healing. It could still bear the rune, so there's that. Please note that these are just suggestions. They do not have to be followed upon.