I see. Well, first of all no one will print that banner at 200 inches at 300 dpi, so there’s no use for your client to check it at “full resolution” I have printed large materials, up to 9 ft and the max resolution requested ranges from 50 to 72, however each printer and printing device has its own settings, I just haven’t heard of such a large size being printed at 300.
Now, here’s a risky idea, have you tried opening the file directly in Preview? Maybe you can open it there and if nothing gets changed make your export directly from Preview.
Also I’m not clear if you are exporting from Illustrator or trying to open the .ai file directly into Photoshop, usually opening the file directly in Photoshop yields better results than exporting from AI.
Best,
D.