Turns out Bruce was serious.
It took about two hours to take all the pieces apart, and break and saw them into pieces that fit into our garbage bin. (Due to other, much more normal waste, we'll have to wait until next week for the last bits.) The cage held up very well after 15 years of constant use, but it was showing its age. It was heartbreaking to do it, both because it means the Finsters are gone, and because Bruce had made a beautiful thing — it was almost perfect. Finster Heaven, although a little awkward to clean in the corners.
So far, nothing looks right now.