Diane and Dave,
We just ran outside and took a couple of photos of the backside, to show you how the support system works underneath the counter and above the refrigerator. Here is how we did it ...
We built the framework from 3 sets of wooden 2X2" struts (painted white with waterproof epoxy paint). The first strut (inner drawer frame) is a rectangle that goes all the way around the drawer, and it is anchored through the fibreglass to the outer drawer frame (finished natural with spar urathane) with stainless steel wood screws and glue (marine Goop adhesive).
The second and third struts (also painted white) are "U" shaped and wrap around the sides and underneath the drawer. The bottoms of all three struts rest on the top of the refrigerator, and they are also glued with marine goop. The tops of the second and third struts are stabilized by pieces of oak trim, and the oak trim pieces are joined to the first strut (inner drawer frame) by a pair of Stanley "L" brackets.
We used standard drawer roller rails inside the framework, and these are coupled with the rails that are attached to the drawer itself. Finally, we attached a couple of lengths of oak corner trim (finished with urathane) inside the framework to provide the supports for the sliding cutboard (white plastic).
There is not much room to work in the confined space between the countertop and the refrigerator, and the photos show that the cutting board slides in-and-out just a few inches below the bottom of the propane
burner. The cutting board also serves to cover the drawer (inside) and keep our silverware from jumping out during travel. The installation was awkward, but it is very solid and the drawer/cutting board combo has performed very well so far.
Good luck with your rennovation, and let us know how it goes!
Steve and Jeanne