The only files in "Internal shared storage > Android > data > mobi.beyondpod > files" were:
beyondpod.db.autobak
BeyondPodHistory.bin.autobak
BeyondPodItemHistory.bin.autobak
PlayList.bin.autobak
TrackState.xml.autobak
And my phone didn't recognize .autobak as a filetype associated with any app.
Seeing as though I had only probably added maybe one or two feeds in the last two months I knew all I was really losing with that two-month old backup was the Playlist that I'd added to so I restored that backup. Worked great!
Cleaned up and added what I remembered I'd done since the backup so all is back to normal. (Although still experiencing the white screen freeze upon startup sometimes along with feeds not updating hourly as auto-scheduled.)
This incident has now turned me into a fastidious daily backup fanatic. A future feature idea is the ability to auto-schedule backups to occur daily (or hourly or weekly) that would automatically share to Google Drive so in the event this occurs again (or if the phone bricks) all is saved.