My '73 Argosy has the same extruded molded plastic piece as your unit; the light assembly is separate from that. I've got 6 screws, 3 on each side, that hold the light lens to the assembly. When you remove the lens, you can get to the assembly holddown screws -but you must have already done that since you know the condition of the bulb socket.
I think you've got to remove the light assembly to examine the backside of it to know how the socket is anchored to the plastic backed assembly. I bet there is a metal strip running from side to side to which each of the three sockets are attached. The metal strip should be attached to the assembly's plastic back. If that is how it is done, then you'd probably solder the new socket to the metal strip.
My sockets are in fine condition, but if the rain ever stops in Richmond, VA, I will take a look at my assembly because you've got me wondering about this.