How can I remove the drip rail trim on a '99 TK Magna (around the door frame, over both side windows)? There's a bit of rust beneath it and a new one will cost over $200 if I stuff it getting it off.

Look at the rubber in the door frames. At the three ends, there are pins that need to be removed.
Unpeel the rubber gently, noting how it is held in. It is all one piece.
You will see screws holding the chrome trim to the body. Remove these. Remove chrome trim. Remove more screws. Remove more chrome trim.

And be very gentle. The trim is in one piece and is easily bent/distorted.