I once did extend the screen panels, putting a third one next to screen and help. But that was mainly by javascript. So you can remove them with javscript I’m sure. There were no hooks or so, that’s why I opened a ticket as well with a patch because I thought that it would be useful to have. I got some traction lately, so maybe this feature will be implemented in 3.1 / 3.2:
Maybe the patch still works so you can apply the patch and use the hooks.
Some kind of related / master ticket is: