Did the same to 3 access panels in our Timber Ridge. Got tired of taking out 4 to 12 screws to check or work in the areas blocked off.
Different method, same result!! Cut the screws down and used flat tin nuts to keep screws in panel. Countersunk where the screws went into the corners of the cutout slighty (could still use new screws if wanted!), and used velcro at the 4 corners for retention. Sticky velcro, but stapled the pieces to keep secure. Looks normal, and easily opened with a decor matching knob to grab.