It is not really the Get Info trick that is the issue. I do that procedure on the files after they have been transferred to my phone. As I mentioned, I have iTunes looking at the audiobooks "On My Device" when I do the trick. When the local copy of an audiobook is deleted through Overdrive because it is past due it does not affect my iTunes library because I do not have my files linked there. You mentioned, "Then in iTunes, I do Files and Add Folder to Library, picking the newly downloaded book subfolder..." So, since Overdrive will delete the PC copy of the audiobook files, and since those files are incorporated into iTunes and hence will be deleted from iTunes, the next time you "sync" the files it will be deleted from your phone. In other words, if there is a file in iTunes that is synchronized to your phone and you delete it from iTunes. it will be deleted from your phone.
I did not realize that this was the case until someone in this forum pointed it out several years ago. I had always used Overdrive per there FAQ instructions/examples. They explained how to transfer books to the iPhone and that iTunes had to be running in order for that to work. Overdrive is one of those programs that sort of goes around iTunes and communicates directly to the phone. It still needs part of iTunes to be active (drivers or some API?) to do the transfer, but that is all. The Overdrive instructions that I learned from just said to open iTunes before the files are transferred to the device, and wait for all of the files to be loaded onto the iPhone, and then close iTunes. There were no other instructions about doing any operations in iTunes (except the one-time setup of the bit rate for audio). I remember this pretty clearly because it was back in the days that iTunes would not close if another program was using it. The instructions said to be sure to close Overdrive before quitting iTunes or you will get an error message. In any case I had never noticed that I had to delete the audiobook files manually from my phone or else they would never go away until I read that post. I had never noticed it because I always delete books that I have listened to before transferring new ones.
So, unless things have changed, I expect that they will be taken off of your phone the next time you enter Overdrive and then sync.
I wonder why you and I seem to be among the few that are not having trouble with iBooks. A few days ago I read the first 5 or so pages of this topic before posting and it seemed like everyone was have trouble with the position marker not moving, the position being lost, and the 15 second replay/advance buttons not working properly. I wonder if this has something to do with books that were already on their phones or something. All of my books were manually transferred and manually set to the Audiobook media kind along with having the "Remember playback position" box checked for each part of each book..
It would be nice if one of the people that are having problems would connect there phone to their PC and select all of the parts of an audiobook from the "On My Device" list. Then "Get Info" and go into Options and set the media kind to Audiobook and check the "Remember playback position" and "Skip when shuffling" boxes. This seems to be working for us.