How can I sync podcasts (with progress) to my Android device with iTunes? I am a user of OS X, and would like to sync my Android device with iTunes.

I still use an iPhone and have a bunch of existing podcasts, and sometimes I use desktop to listen to podcasts, so two-way synchronization of files as well as progress would be quite useful. By progress I refer to time as well as whether an episode was completed. There is no need to sync with iOS devices directly; syncing with desktop iTunes on OS X is perfectly fine.

Any app that I found so far that even has sync apparently can sync only with itself on Android and iOS, but not with iTunes; or else it can import audio files from iTunes, ignoring progress.
DoubleTwist was built for a similar purpose and does the job well. To use it, you can simply install the Mac app and the Android app and use their DoubleTwist Sync feature to synchronize iTunes with Android.