I’m a bit baffled by your baffle?
Is the rubber patch sealed on all four sides?
I’m suspecting it may serve as an air-release or air regulator? It would keep the reeds from the shock of getting a full blast of air (something I’ve done many times when I’ve accidentally hit a key while blowing out the moisture),or possibly it’s to equal out the volume as no one note would ever get a full serving of air.
Have you tried playing without the cover and feeling to see if any air escapes from around the flap or if it’s sealed does it seem to expand like a balloon? Also if you aren’t afraid of damaging the reeds have you tried playing as hard as you can?