I have a 2005 39S Excursion which is 99% the same as you Discovery.
After removing the four bolts, look at the carpet on the floor against the left hand wall (left wall when your head is in the closet). On mine, they gave some dummy kid a pneumatic carpet stapler and told him to secure the carpet. There were probably 75 staples over there that I had to pull out before the hatch would rise.
The hatch is not glued down, but there is a large rubber gasket under there to seal the hatch so engine fumes don't rise into the closet. This means you'll have to do some prying to get it up as the engine heat and time as "sealed" it to the lid. I'd recommend about four 2x4 pieces stacked in front of the closet to pry from so the pry bar isn't pressing into the front of the closet molding.
If you have any hooks in the rear wall like for holding the extra leaf for the dining table or the extra chairs, you will probably have to remove those from the wall also.
You really only want to get in there one time which is to change the belts, possibly the hoses and to have the engine coolant flushed and the have it filled with an ELC coolant that will be good for many years.
Also from the outside rear look at your coolant overflow tank on the upper right corner of the radiator. When they made these, they used bad plastic and most people had to replace them because all of the small heat cracks start leaking - had to do ours in Billings Montana. The truck shop had them on hand, but it took two days before they could work us in and then we had to unload everything from the closet - you can't change the overflow tank from the rear because of the hose connections that are on the inside, under the engine cover.
Also, if you haven't noticed, on the right side of the rear closet there's another small hatch that opens up. This is where the air intake hose for the engine comes in. Make sure the connections on it are still tight. Also, this hatch makes a very good place to store emergency belts and filters for the main engine and generator in. I keep my "working stock" of filters in one of the compartments. There's also room in there for other spares that you hope you never need like rebuild kits for the shower and faucets.
As mentioned above, you don't need to raise the lid for filter change. As a matter of fact, I'm sure you cant' change the smaller fuel filter from up there. You need to do it from below and have long arms.
And while you have the engine lid off, use your camera to take lots of pictures. I always have questions later like what's the amp rating of the alternator or what's the part number on it if you notice it starting to go bad on you. Take pictures of these things.
Bill
Nodwell RN110 out moose hunting. 4-53 Detroit, Clark 5 spd, 40" wide tracks, 10:00x20 tires, 16,000# capacity, 22,000# weight. You know the mud is getting deep when it's coming in the doors.