correct me if I am wrong: each character graphic = a single character, and multiple of his graphic = different versions of him pulled from different universes?
More or less, yes.
An idea might be to create a "meta personality" that encompasses some global statistics (benefits, negatives, whatever) relative to that specific character graphic ("Martyn", as the case may be); the player's "slice" of Martyn accrues benefits, some of which benefit every Martyn in the multiverse; so, for instance, if Martyn 1 died and the player created Martyn 2, some (not all) benefits might remain. From there, I can envision two possible branches (I'm sure there are more, this is just off the top of my head):
1) A la a Hollywood movie I once saw, there are a limited number of Martyn's in the multiverse - the story explanation for this is left as an exercise to the reader, but the gameplay ramification is that they cannot run around all "willy nilly" and waste Martyn's left and right; the implication is that they could not waste slices of any multiverse character, either. However, a possible twist (as per the Hollywood movie) is that the less Martyn's there are, the more powerful the remaining Martyn(s) become - the gameplay ramification being that the player has to manage their pool of Martyn's to meet their gameplay objectives - a single powerful embodiment of Martyn, or several mediocre Martyn's. Depending on the nature of various enemies in the world, this sort of gameplay mechanic might offer an implicit bonus/penalty to certain play styles.
This next point may or may not make sense, because I am relatively new to AVWW, so bear with me ...
2) I've noticed an increasing focus on missions; so, perhaps the players slice of Martyn accrues some abilities that allow him to effectively modify a mission in certain ways (maybe handicap a specific type of enemy, or all [mini]bosses have a permanent movement penalty), but this bonus is only for the players slice of Martyn and no other; if the players Martyn dies this bonus is lost until it is gained again (in some unspecified fashion). This is separate from the inventory, so there is no dreaded corpse-running, but also is tangible enough that the player will really feel it - permit me to be longwinded and elaborate here.
I, the player, control a specific slice of Martyn - we will call him Martyn X. Martyn X has, through unspecified means, acquired the ability to modify various mission parameters upon engaging in a mission - this allows him to tackle higher level missions than might otherwise be possible. If Martyn X dies, I can no longer attempt such high level missions and my progress is (significantly?) slowed, without having actually lost any inventory item, spell, etc.
Just some ideas.