Thanks for the "How To" here!
I just did it this morning, and instructions were a great help. I was surprised how much dust was behind the door panel though, and inside the door panel. Later I'll look and see where it might be coming from...other than age *LOL*
my notes (I have a 2004 GX-470):
Where you reference the different direction to unsnap the panel(s) I only saw the need to move "toward the rear wiper" on the top (and if you push it, the side...) panels above and on the side(s) of the window. The whole lower panel came off with the one screw you mentioned (although I had no idea a first-aid kit went there, mine was/is missing), removing the pull handle as you described, and prying the other clips straight forward, away from the door frame.
I replaced the whole reverse-light module, mine was cracked, so same process, but in addition, there were only two bolts to remove, and the bulb and housing.