BlockUntilSyncedToCurrentChain: txindex is catching up on block notifications
One way to solve this seems to be to disable and then reenable txindex. In other words, stop bitcoind, set txindex=0 in bitcoin.conf, start bitcoind, wait until fully started, stop bitcoind, set txindex=1, start bitcoind, wait until message "txindex is enabled at height xxx".

Unsure why this is necessary though.