Also infuriated by this change. They've really gone out of their way to make Podcasts unworkable on the iPhone. After years of persevering, thinking "I must be using it wrong, Apple would not design it this poorly", I've recently deleted the Podcasts app. I got sick of it not syncing with iTunes, wanting to keep it's own record of downloaded/listened podcasts, sneaking in costly downloads, losing its place, stopping, skipping and generally being infuriating.
I attempted the solutions posted earlier in this thread - basically, deleting Podcasts on the iPhone, then setting up podcasts in iTunes on the Mac as usual, letting it download, then selecting them all and changing the Media Kind to Audiobook. I found trying to mark them as a Voice Memo to keep them separate doesn't work - Voice Memos aren't synced to the iPhone. Changing them to Audiobook and setting the genre to Podcast allowed me to create a Smart Playlist on that metadata with a play count of 0, and sync to the iPhone. All looked to be right with the world!
Unfortunately there are several gotchas: the first is that a confusing combination of sync options means all the podcasts will probably get synced twice, and in my case, the storage on the iPhone gets exhausted. I think there's a work around - select the iPhone in iTunes, go to Podcasts and uncheck "Sync Podcasts". Then in Books, selected "Sync Audiobooks" but change it to "Selected audiobooks" and only select the Smart Playlist you created. Not sure if this is going to work reliably, but it seems to have addressed the immediate problem.
The major problem however, and it's a showstopper, is that as soon as you set all your podcasts to Audiobooks, iTunes gets to work re-downloading them all. So not only do you have a constant download leak, you end up with multiple copies of every Podcast, rendering the "play count = 0" trick meaningless! I haven't found a way around this yet. It's so frustrating - I just want to listen to Podcasts like I used to be able to.
FWIW, there's a parallel thread on the same topic, with the same findings, here: music app - podcasts iOS 7