I would hack the area out using a demolition saw . Use a fine blade . Stick it down with 3 day , off gassing , industrial glue . Something that is used in road construction. Cover with silver tape . Using weld wood , stick on a layer of plasterboard . To seal it , cover it with black gorilla tape . No need to be neat . Don't forget to paint it white so it doesn't get hot . Then , a couple half inch coach bolts through the board . Make sure the bolts are stainless so they won't rust . If you can't afford stainless , gal works , but have to be replaced every six months . If your thinking of keeping the board for more than two years , stainless is more economical . Don't for a second consider high tensile bolts , although the strongest , they will rust after one use and make the repair ugly . Don't forget to put a couple bolts through the other side to even the weight . As a bonus it will prevent the other side from delaminating. Finally cure in the bathroom for 3 days with the fan on .
Im sorry , couldn't help it .

Its OK , he won't do it . He can't see this , I'm blocked .
ps: this post is for amusement only , not a recommended board fix .