Is there a way to position a button within a vertical or horizontal group in the middle of the screen, similar to the descendent screen in Rogue Legacy?
I haven’t found a viable way to do this using the built-in UI tools.
Can you explain more? You don’t event need a layout group to place a button in center of the screen using new UI.
Something similar to this: 
To ask again: is there a way to do something like this using the latest 4.6 UI tools?
You can just align the button to the center of the canvas or screen but place it in a layer above the scrolling region.
So have the actual button to be interacted with in the center of the canvas, but have the choices on a layer drawn below the button. How does that solve the issue of actually moving the choice to that position within the scroll rect?
Unfortunately, this has to be custom coded.
It shouldn’t take much in the way of coding you only have 2 states, scrolling and stopped, you can animate the scrolling effect (3 states if you can scroll both ways). Then you just need a column of 3 items that you can scroll and change the text/images on.