The first sentence of your petition"The locked bootloader prevents the phone from being rooted", is completely wrong.I created a petition on change.org to try to get T-Mobile to unlock the bootloader. It might be a longshot, but wth.
http://chn.ge/1k6HIYx
Here's the link to the thread I created on XDA
http://xdaforums.com/showthread.php?t=2753060
Having a locked bootloader is not the same as rooting. I have a Sony Xperia Ion. It has a locked bootloader but it is rooted.
You will need to fix that immediately if you want Sony or T-Mobile to take your petition seriously.