If you can get the screws back in the holes, you can get a drill bit or Dremel tool bit into the hole, and drill it out. (You might have to use a right angle drill, or a long bit.).
No, the factory never did it right. There are very few factors which do it correctly. It is being competitive. The factory would probably charge several hundred dollars more for the boat. (I think it would be worth it.). Some better builders put solid glass or a substance like Coosa board into a place where there will be screws or bolts.
The C Dory is unique, in that it holds its value--or at least for the time I have been involved (about 20 years) they have held their value. (Of course there is this inflation--which is more now than any time in the last 30 years.)
If the boat stays in a dry climate, a non freezing climate, or is kept in a covered climate controlled storage then there will never be an issue with screw into the core.
In your case, you have introduced a different factor. The boat is now in a freezing thaw cycle climate. That is often where problems arise. A little moisture gets into the core, expands and then contracts, more moisture comes in.
Most likely there are other issues with screws into the core--for instance your boat will have the "L" brackets holding the wood furniture in place. In some of my boats of that vintage, I have removed those "L" brackets, and replaced them with taking in 1708 glass, with an epoxy, which seals the hole, and makes a good bond, to be stronger than the screw and "L" bracket. If you ever want to re-do the interiors then you can easily cut the "tab".
The C dory is easy. When I bought My Cal 46, I pulled all thru deck fittings, including a 48' teak toe rail, lifeline stanchions, thru deck fittings and epoxy plugged all of these--hundreds of holes. Why? Because I have done some studies on the cored hulls, and delimitation.
Enjoy the boat.