Looks like I have a couple of flys on the inside of the screen

Dont even think of removing the screen.....virtually impossible to reinstall. If you must clean...clean the picture tubes. Blow the dust off the lenses with air spray, then spray a lint free cloth with a lcd, plasma cleaner. Try not to use windex. [leaves a film on plastic lens] . Now pay close attention because the mirror you try to clean is a reflective plastic sheet that can tear easily. Lightly brush a new feather duster on this. Now you can only do this by removing the lower back cover [a hard cardboard material] and dislocate your elbo to clean . You can clean the inside of screen with the feather duster, donot use a cleaner inside the screen or mirror. Relocate the old elbo and replce the lower back cover.