Thanks for the helpful hints guys.
I took the door panel off again, sprayed all the mechanism with "Gunk Engine Cleaner", wiped off all the excess I could reach and then sprayed it all with WD40.
It has never worked better.
We'll see how long that lasts.
I might even do the passenger side as part of preventive maintenance.
And of course now I know for sure that my anti-theft alarm doesn't work.
Just one more mystery to solve.
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