I figured out the signal. It is in fact Manchester encoded with 16 start bits. Thanks for the tip about Manchester encoding MrMark.
The CRC is CRC-16/BUYPASS. I found it with http://reveng.sourceforge.net/. There are many different kinds of CRC, so unless it is one of the more common ones (which it is not), a tool like reveng is needed.
I still have to work on demodulation and digitizing, but right now things look good.