I was blown away by how similar some of our ideas were, like having co-op and competitive 2 player modes, and having one of several pokemon companions that allow you to interact with wild pokemon.
One of the few issues I had with the original was the linearity and repetitiveness. I would overcome this by having a store where you could spend points from photos to buy new equipment and unlock new areas in an order partially determined by the player.
Also, connecting levels so you can switch levels mid-run would allow you to travel through the same places at different times, when a new event or pokemon may be visible. Certain events may be triggered in one level and require you to switch to another level to see the event. A time limit could keep multi-level runs short.
You had mentioned that you had more ideas, I'd love to hear them! Send a message anytime.