So, it seems like it actually is possible to write data to the 540 with the TN command. It only works on channels 5+, and it still returns an AK F (failed) message. However, it's possible to then retrieve these times from the 540 using the RT command.
Sent: #TN 0016 0072 05 12:13:56.7800 12345 06D9
Received: AK F 00F2
Sent: #RT 0072 05 0292
Received: AN 16 72 M5 12:13:56.77984 2345 06D6
It won't work without sending the correct checksum to the 540 (06D9 in this case) followed by a carriage return and a new line. Hope that helps!