Here's where development is at the moment.
I put the stack on the right, and the saved view sets on the left. The stack automatically gets the name [layers]/[renders], without extra labels. This way the label in the stack is small, and any extra room can go to the named set on the left.
Here is a little guide on the stack label format:
3/5 - 3 layers are visible and 5 renders are visible
2/ - 2 layers are visible and renders will be unchanged
/4 - layers will be unchanged and 4 renders are visible
0/3 - 0 layers are visible and 3 renders are visible
Note the subtle distinction between "/4" and "0/3".
The "tooltip" for the stack buttons list all the visible layers in the set: