I think I may have solved this age old question (but I need someone with a 2010 or 2011 model Sharp who has updated their firmware to test)!?!

On Sharp's site, I discovered a user manual for the 2012 TVs and it includes commands to do anything the remote can! I now have a 2012 model (returned my 2011 Sharp 735u), and I'm working on a module for my home automation system to use the commands.

I'd love to know if this 2012 protocol works on some of the older sets.

New manual: [Link: files.sharpusa.com]