No screws on my 02. There are 4 little posts that hold the panel into place. I remove it by gently lifting equally on all 4 posts until it is free. If you need to take it off completely to repair or replace it, there is an electrical plug you can disconnect after it is opened up.
Getting it back together is another challenge. On mine, the 4 posts on the underside of the panel have to be aligned with the slots they fit into before the panel can be pushed back down all the way into the "self locking" slots. The cover also has kind of a tail section (I have no clue what it's called) that has to be tucked under the open area (back by the parking brake) before attempting to line up the clips and slots. For me, it's easier to reassemble when the gear selector is in neutral (just press the round solenoid thingy and you can move the gear selector while everything is opened up).
The first few times I needed to open up the area, I removed the cupholders for better visibility and a bit more manuevering room. Now I just do it "by feel" since my solenoid never locks up in a convenient place or time. I do understand your hesitancy to pull hard because it does take so much effort that you feel like you're going to break it. Just be ready to catch yourself from smacking into the windsheild when it does finally pull loose. That's the reason I sit facing backwards on the passenger seat to remove it.
Here is a pic that illustrates that location of the posts and the tail section on the underside of the gear selector cover. Hope that helps
Good Luck, Jamie