SurlyOldManMN was right. Took less than 10 minutes to do this; 15 actually because I wanted to clean out some leaves and junk. Besides, it's very satisfying to take stuff out of the car.
The rubber gasket is really soft and pliable, so it's no wonder it folds in on itself. Here's a shot of the engine bay with the IC and hose gasket taken out.
Sound issue resolved! Thanks, guys.