I think to make it work well, you would need some kind of spacer at the back of the rails.
Perhaps two wooden dowels cut to the correct length with small screws passed through the rear holes of the rails and driven into the end of the dowels.
You could also try bending the mounting ears out a bit, and seeing if the "springyness" would hold the rails engaged in the slots at the back.
I think to make it work well, you would need some kind of spacer at the back of the rails.
Perhaps two wooden dowels cut to the correct length with small screws passed through the rear holes of the rails and driven into the end of the dowels.