In addition to @rmschne’s astute suggestions, have you verified the database in DEVONthink To Go by long-pressing it on the databases screen and choosing Verify & Repair?
I had never heard of that. (I mean, on iOS. I V&R all the time on desktop, of course.)
And … it seems to have done the trick. After verifying and repairing as you said to, iOS database is back in sync.
Thank you! Very glad to learn about this.