Ok then. To answer my own question 10 minutes later:

1. Grit your teeth. Grip the housing.

2. Pull it forward hard while twisting it downwards about 10-15 degrees so that little tab points right at the corner of the opening in the wood.

3. Hope hope hope it doesn't break.

4. Keep going until it pops out. The tab just clears the wood as the housing slides down the handle.

And bingo, the door panel's off.

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1988 420SEL