I also tried Overcast & didn't like it. That is why I tried RSSRadio (and others). It has a free version (with banner ads at bottom) and an upgrade to remove the ads. It has tons of settings (they are mostly useful and can be applied per feed) but I think it is pretty simple once you learn how to use it.
Option 1
I haven't tried Google Drive. If you really like that as a solution you should investigate 'workflow' apps or workflow services. I suspect an IFTTT job could see new episodes in a podcast feed & save them to a folder, otherwise Apples Workflow app may do something similar (not tried any of these, just a thought).
IFTTT helps your apps and devices work together - IFTTT
Workflow — Powerful automation made simple.
Obviously you are now 'reinventing the wheel' and you may have weird edge case issues, like when an episode gets reuploaded or feeds get redirected etc.
Option 2
Dropcaster is a script to create a podcast feed from files in a folder (intended to be in Dropbox, but GDrive may work too). GitHub - nerab/dropcaster: Simple Podcast Publishing with Dropbox
That could be another option I guess. This assumes you still want to download from a feed.
Option 3
If you are intent on syncing downloaded files from iTunes on a computer to a device you can consider changing the media type of episodes from 'podcast' to audiobook or music (get info in iTunes). That will cause them to sync to the Audiobooks app or the Music app. That is a horrid workaround IMO but sometimes you have to do what makes you happiest 🙂
These seem convoluted to me, I don't understand why you cannot grab episodes via Wi-Fi on the iOS device. Does it have to be synced from iTunes?