Some other options...
AudiobookCD Free does what I want. It has ads, or you can pay 99¢ for ad-free. You can pause from the lock screen, which is nice, but it only has 30s rewind. I am using the free version for now and may get Ambling player if it goes on sale again.
https://itunes.apple.com/us/app/audi...515773933?mt=8
On Cue Player (99¢) will do what I want according to its author, but it is no longer being developed.
https://itunes.apple.com/us/app/on-c...403200500?mt=8