parametric curved drawers

Hi all, newbie here (of  course!) 

I am trying to make a curved drawer face. I would like to make it parametric. I am finding it very difficult to sketch. One parameter will be the width of the drawer opening, the other would be the desired radius of the curve.  The drawers will be made from bent laminations and I want to explore the design before I make the forms to do the bending.  

One awkward solution I came up with was to lay out the sides (thus the opening) and then use a 3-point arc . The issue here was that I could not figure out a way to specify the radius other than moving the mouse when defining the 3rd point, watching the radius in the bottom left corner, and stopping when I was close (I never nailed the exact radius). Moreover this solution is not in any way parametric.

I then tried creating a circle and a rectangle and tried to cut an arc with limited success.

Additionally, the drawer face will nominally be 3/4" thick with a certain radius. I say nominally because the ultimate thickness will be determined after the glue-up is done and I measure the actual.  The drawer itself will also have a curved front that the drawer face will attach to.  It will be concentrically smaller than the drawer front (and its width will be narrower to accommodate the side-mount drawer slide hardware. I want the front part of the actual drawer to be parametrically related to the drawer face. My question is what would be the preferred approach to sketching this out?

Below is one of my studies:

https://a360.co/41XVokE

Thanks, Steve