Prior to 1985 (?)the metal plate that went underneath the bezel was set up for the two-knob radio, and bolted to four 'u-nuts' set into the sides of the dash opening. When I made the swap 20 years ago, I made a plate from 1/8" aluminum. I placed the radio into the dash opening and figured out how it needed to fit. Then I transferred the measurements to the aluminum plate so that the slot for the radio sleeve was in the right place to hold the radio in the opening. Then I transferred the dimensions to the radio bezel (mine was a two-knobber) and carefully cut the bezel with a short straightedge and a razor. The decorative 'wallpaper' peels off, then I filed the underlying bezel plastic to the exact dimensions of the cut in the 'wallpaper'. The aluminum holds up the radio. Since you will be going with the bezel intended for flat-panel radio, consider centering the cutout in the aluminum so it looks nice. you'll judge your work every time you look at the radio. I painted the aluminum a semi-gloss black to help it match the radio trim. Don't forget to bolt the strap on the back of the radio to somewhere in the back of the dash to hold up the radio. This way it won't loosen up the sleeve, which depends upon folded-back tabs to keep it in place.
This is old data, so I may have forgotten the swearing I'm sure happened at the time.