There are hidden screws behind the elbow cushion. Also behind the bezel that has the tweeter.

Then around the sides and bottom there are those push in clips that you need to pry out. Use a plastic flat pry bar or a panel removal tool...pry close to the clip.....dont flex the panel too much. It will crack.

The top side mirror trim pc also must come out, as once the panel is fully lose, it comes up and off.....there is a clip over the top of the door where the glass is....all along the top.

It is so stupid that gm got rid of that tweeter location......what morons. I miss that big time.
Grab yourself a nice set of 6.5 inch components and some 4x6's for the rear sound bar if you have it......then a 5 channel amp, and a sub. Hey Its Christmas!!!!

 

And try to do it in warmer temps. The plastic panels will be less likely to break. As for the elbow cushion, it may have small screws holding it down, in combination with spring clips. Heavy (10mm?) bolts will be underneath.

While it's better than having the tweeters at the bottom of the door, acoustically speaking, they are still a little low. The closer to ear level is best. High frequencies are very directional.

 

The 96-02 panels, like yours, actually slide up about an inch to remove them, rather than the usual press in clips. Remove the two screws in the armrest and take it off, take off the two screws by the door handle (one is hidden by the snap in plate), and remove the piece at top front (it just presses in).

I didn't know either until I saw a youtube how-to video on changing the inner door handle.

The pod with the power window controls can be removed from the panel, it presses in with two clips a few inches up from the bottom, and snaps at the top. Mine has one snap broken on both sides. There's probably a tweeter in that pod that's installed by melting the posts it attaches to. They did cast a second set of posts that look like they'll take the same small bolts most of the rest of the dash uses so maybe there's optional versions. I plugged a set in on mine but they don't seem to get any audio (it didn't have any before).

I looked at a 2003 door someone ripped up in the junkyard and it looks like those go to the standard pop in plastic pins.

 

 

 

 

Nothing lasts forever.

Is there a capacitor on the tweeter? There should be some sort of crossover to help guide the correct frequencies. The passive way to do this is to put a capacitor on the tweeter to limit low frequencies. The active way is a circuit board (in a box), possibly in the door. But your best bet is to replace it all. Finding a 6.5 that will match the tweeter will be difficult at best. And a set will come with a crossover. This is what I got;

 

 

And that's what happens when I forum late at night. Looked right at it, didn't see it.