So it came down to this: either throw away all of the toys, or find some way to lock them away so that I can have control. We came up with the (rather expensive) solution of purchasing plastic bins with lids from Walmart and gigantic wardrobes with shelves from Ikea. And so, $600 and some serious hard labor later, I have a newly organized toy room.
Our new rule is they can each play with one bin at a time. If they want to play with something else, they have to clean up the first bin before they can get another out. And again, without the locks there is no way this system would work around here--not with these two around.
I am mad at how blurry this picture came out, but it is still cute.