Oh man...
I'd love an answer to this. I have two Wii U Pros and things just don't work right when I attempt use them both.
They are both registered devices via the onboard BT. As you said, they both show as being player 1 on each controller.
The wife and I get lots of crashing, random button presses, and even phantom rumbles from the unused controller when it is just sitting there. My solution has been to just disconnect one and not use it. But, that sucks.
I'd love to be able to use two Wii U Pros at the same time....
Thanks.