The solution seems to be that BitTorrent Sync should be running whilst starting Resilio Sync. It is strange how things work out when you decide to complain about it. The lesson is: always complain about everything.
I used BitTorrent Sync on Android 6.0.1, I was told to "upgrade" to Resilio Sync. Installed, clicked Start Migration, Allow SD card access.. Shows "Restoring Identity" and never completes. If I stop Resilio Sync and start BitTorrent Sync again, it all still works.