I've only had mine off a couple of times. I can't remember what I pulled on them with, but I just now looked at one of the old handles and sure enough it looks like it just pulls straight up. I know there isn't much space and it looks like it can't be done, but it can. Pull the plastic surrounding piece (about 3"x5") off first. This will give you a little more room. Carefully pry it off. Squeeze the top and bottom edges toward each other. That helps it clear the little tabs that hold it to the inner plastic piece. There are three plastic pieces of the same color for each handle: the little one you grab to open the door, the outer surround (about 3"x5"), and the inner "bowl" that the handle is nestled in. Good luck.
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Thanks to everyone for the help, Doug C. 81 242 Brick Off Blocks, stock, M46; 86 244, 140k , auto.