I didn't realize stand-alone was the same thing as single-user mode –– are you sure? I guess I don't know what the alternative is to "a stand-alone backend."
The server is started using a straightforward call to "postgres". It's not using the --single flag, which is what I assume is needed for the single-user mode.
I followed your instructions above and modified the pg_hba.conf in master to hardcode the IP address of the standby server. I kept the same pg_hba.conf file for the standby server –– I hope that was right. The log output hasn't changed much, but I'm enclosing it in this gist:
If you get an error after making that change, then please attach the complete new version of the pg_hba.conf AND the entry from postgres log where it complains about the invalid or non pg_hba.conf entry.