What I am trying to achieve is a rounded corner slope towards the bottom between the inner top edge of the cube and the middle edge.
I Have tried selecting all the segments composing the inner edge of the cube and using the move tool to move it down but it doesn’t behave the way I want it to.
You can do that. Select all inside edges at the top, start move and then hit the UP arrow key. and move the edges down. I would not call that “rounded” though
For rounding I would draw an arc at the inside edge. I am using X-ray mode to draw within, then use follow me tool. I have to take my view inside to select the face to complete the operation. Afterward I may have an edge or two to delete.
But since I use plugins I am most likely to use Fredo’s Round Corner tool instead–last picture.
Basically your inner edge is just too far in for the faces to split cleanly, sketchup tries but is confused.
Note in the give how the split donut tool does some long diagonals. By using one edge and split sausage I force it to break the face uniformly.
Yes, Split tools is an extension available from Sketchucation, I can give you a link if you want it but I was using really just to show the issue.
Would not follow me be a more appropriate option.?