I was thinking about this some more today, and I really think the Caped Soul/ possession idea is the direction I want to go with this game. There are all kinds of unique experiences you could create with this idea, and deciding what to possess and in what order will make the game experience different each time you replay a level.
The idea of possessing statues, not just enemies, is something that really has potential I think. For example, you know how several games have statues of heads on the dungeon walls, which spit magic balls or arrows? Wouldn't it be cool to possess something like that and snipe the enemies on the map? How about statues of guards at the entrance to a palace? Or possess a gargoyle statue and go on a rampage!
It would be important to limit this power somehow, or the game would just be too easy, and no fun to play. One idea would be to make it so possessing something takes some amount of time (targeting and then staring at at the target, for example). The more powerful the target, the longer it would take to posses. Fast-moving targets would be very difficult to posses, but would be a huge advantage if you can pull it off (flying enemies, for example, to skip over difficult areas of a map).
I also like the idea of making the ultimate enemy to be other creatures like yourself, who can also possess things. It could be used for some very exciting bosses at the end of the levels - utilizing the environment through possession to attack each other!