|It is entirely possible that despite your best efforts, the new backing plate will rot, but in another 36 years, that's unlikely to be your problem. I'd use plywood and bed the drain fitting well so it won't let water through; if you're concerned about rot, you could coat the wood with epoxy. If you're dead set on ignoring the advice in the first sentence, you could use Starboard (a vinyl board) or multiple layers of fibreglass.
Of greater concern is the hose that joins the drains and through-hulls below. When I bought our '82 boat in '97, the surveyor immediately condemned the hoses due to visible cracking; these are normally very expensive, but a forum member reported that he was able to get replacements for all his underwater hoses at a very good price from marine discounter Defender Industries.
Fortunately, Mk IV's have real seacocks and these were renewed with a good cleaning. Many older C&C's have through-hulls topped with brass gate valves. These may be corroded, so make sure they work before replacing the hoses. If they don't work, let us know and someone will doubtless point you to the many discussions of their replacement.
C&C 27 Mk IV