30 years is a long time to find a perfectly matching replacement. I replaced my 40 year old ones, though, and it wasn't too bad. I forget exactly what I had to do, but it wasn't hard by any means to make them fit. It's easy to make the hole a bit bigger or rotate the ring a bit to relocate the holes. Making the hole smaller takes a bit more work
The spec for the access plate is the opening size not the outermost measurement. In your case it looks like a 6 inch model.
Here is a link to the Beckson catalog pages for pry out plates.