I've figured this out on my own. Feeling kind of silly, although I think I'll lay at least part of the blame on the quality of Sony's instructions.

1 - You must issue the "standby command enable" command while the set is already powered on. You can't do this when the set is powered off, as I discovered!

2 - After issuing "standby command enable" while the set is on, use the "power off" command to turn off the television (other methods of powering off may or may not allow you to power back on later; haven't tested yet).

3 - If you issued "standby command enable" before powering down, you should be able to "power on" now using the appropriate RS232 command.

A frustrating few hours to be sure, but thankfully met with a happy ending. I think it's time for a beer!