Well, as per someone with too much time on their hands, I made a mock-up of an ejection port cover.
Before you guys bash it, just remember it is a crude, unrefined model of something that someone here with machining skills/tools could professionally do. And no, it isn't made out of aluminum foil. It's sheet metal...
Thinking about how one could fasten it to the side of the gun, I think the best option for not voiding the warranty would be to use 3m double sided automotive tape ( I know it kind of makes me cringe too, but short of a rail mounting system you'd have to screw it in ). The tape is super strong in all weather and would definitely hold something of little weight like this without problems.
Anyway, have a look and please remember, it's just a mock-up...