I've got the latest Powered Up remote, I was hoping it would pair with the Move Hub instead of using the Boost App.
At the moment it doesn't want to pair.
Since June 2019, this is possible. See here: https://www.hispabrickmagazine.com/content/2019/06/03/powered-up-ii-powered-up-ii-networks/
Look right at the bottom of the article.
The latest version of the Powered Up app (2.2.0) as well as the latest version of the Boost app include new firmware for the Boost hub. After this update it is possible to control the Boost hub with a remote control.
Establishing the connection is a little more difficult than connecting a single Powered Up hub to a remote. It is not enough to just press the start button on each device and wait. You need to press the start button on both devices simultaneously after starting them to establish the connection (as if the Boost hub were a second hub in an existing network).
Now you can control the internal motors (A and B in the Boost hub) with the remote control.
This is not possible at the moment. This could be enabled in a future firmware update, but I'm honestly not sure how this would work. The Move Hub has 4 possible outputs. Mapping those to the pair of outputs normally controlled by the current remote seems like it would be somewhat clunky or non-intuitive.
If you use third party software to form a Powered Up network you can pair the remote and the Move hub to a computer and control them both from there. You could write your program such that pressing the green button would change the LED colour and swap between controlling ports A/B or C/D.