Insane characters fitting perfectly into Shadowrun is probably the thing it does best. One of the players I played with in the PbP-game had bees as his weapons, buddies and … everything else, basically. Dr Bees!
Get away from traditional architectures in RPG design, that's my advice. Move toward systems and styles of play which are more distributed and which allow more than they prohibit.
Indeed! This is why I like powered by the apocalypse (and narrative systems in general) so much. If your character is defined by who he is, rather than a character sheet you will have more fun roleplaying, rather than playing a board-game.