Yes, I've solved the problem for my device. What worked for me: (1) Plug the iPhone in to the computer. (2) Go to the iPhone tab in iTunes. (3) "Back Up Now." (4) Select "Restore iPhone", sort of in the top right corner. (5) You'll get another option - I forget the exact wording, but it's something like "factory reset" and "restore from backup". Select "Restore from Backup." And wait, and wait, and wait, while everything gets wiped and recopied. That fixed my problem. My Documents & Data usage for the Podcasts app is now 25.0MB.
Note that because I restored from a backup, I didn't need to reinstall apps or reenter passwords or any of that other hassle that comes with a full factory reset, so although the restore took time, I didn't need to do much.
Caveats:
1) Don't use the Podcasts app anymore. I did a factory reset back in the summer, and that also wiped out the Documents & Data usage, but within a couple of months it was up to 3.0GB again. I suspect that if you continue to use Apple's Podcast app and already have this problem, this memory bloat is inevitable, and you may give yourself a few weeks of freedom, but it'll come back. I now use Overcast, which I highly recommend as long as you use only audio podcasts, and listen only on iOS devices. (If you need to sync with your computer, I don't know what to suggest, and can only wish you good luck! I gave up on that years ago.)
2) Don't select the "Restore Backup" option that appears in the middle of the iPhone sync page in iTunes. I did that one before, and it didn't work for me. I don't understand why choosing "Restore iPhone" first and then "Restore from Backup" is different from simply "Restore Backup", but so be it.