So, I updated to 9.0.2 and I shut podcast syncing off in iTunes. On the plus side, the app no longer crashes instantaneously. On the downside, it now takes three minutes (I exaggerate -- 2m 53s last time) of "Updating" before it suddenly crashes. Best of all, before it only took up about 300mb but now it's up to 1.3gb. I assume that's because earlier I had it set to sync podcasts. But when I go into settings it only shows three or four very small "saved" podcasts and none of the larger flles that are probably lost in the "updating" crash. Since you can't clear the "Documents & Data" I suppose I have to hope that 9.1 fixes it enough that I can clear the app out.
In the meantime I've begun using Downcast. I miss a few things about Podcasts but Downcast makes up for it with other features (like smarter playlists). I doubt I'll return to Podcasts. Ever since iTunes has decided to automatically and quietly "unsubscribe" me from podcasts that I haven't listened to in awhile it's been a pain; this just finally forced me out.