Sorted it out thanks to the folks in IRC. I didn't change any configs, just killed the sender process on the primary via pg_terminate_backed() on the PID of the sender (as seen in pg_stat_replication). This caused recovery on the standby immediately fall back to WAL recovery, where it quickly restored and recovered all the WAL files I had copied over. Once it finished with those, it opened another streaming connection. So I'll just rinse/repeat this process until our networking issues are resolved.
