Am I just out of luck?
Yep, you and me both
People will try and say it is cause of the carriers, yet HTC, LG and Samsung phones on the same carriers are not all locked up. It is the one thing I don't like about this phone, well, that and the viewing angles (coming from a HTC one which had incredible speakers and screen)
So, it seems your phone should be Z1S, that's why all Z1S owners are not allowed to unlock their BL
So, here's the link to install CWM, and also it roots your phone with locked BL
It helped me a lot, although mine is Z1 C6903, but I locked BL and done step by step as it says
Wish you success