I have some pages on my website now with details of various colour spaces, although it does not currently include Protune.
You can get the matrix you need for an IDT using this tool. I am not sure what problems you are referring to with Bradford and CAT02, but as far as I am aware, all current IDTs use one of those two.
I believe that the publicly available information on Protune originates with the “experimental transform” in the ACES OCIO config originally made by @hpduiker, based on “conversations with David Newman of GoPro”. There is no official GoPro documentation on their colour encodings.
You might be better making a “black box camera IDT” for your GoPro, using the method which is in the process of being documented by the IDT Virtual Working Group.