Rather than using plywood ---------- which might rot if wet ------- go to a dollar store and pickup a cheap nylon cutting board.
They come in various thicknesses and shapes ----- round , square or rectangular.
When you find one the right size ------ lay the old one down and trace it onto the new pice. Then lay on the new one ( the one that's too small ) inside the larger traced outline ----- trace out the opening and mark the screw holes ------ cut and drill and you're done.
Looks as though there are 2 stand offs to deal with ------- you might be able to cutoff the old ones and expoxy ( or duct tape ) them to the new piece ----- then and again it may not be a big deal if they were glued in place.
Just a thought.