As I mentioned in an earlier post, I only have a Lynx 1 as well. I can insert the game, door still on, without any trouble. As for removing the card, it can be gently wiggled free with small pliers gripping only the upper corners of the EPROM. To prevent damage to the card or label, I've placed a small tab of electrical tape on each corner where the pliers will grip. The tape also prevents any electrical transfer from the metal pliers that could fry the game. So far this has worked out fine for me and I haven't needed to remove the door.
Just a suggestion of how I got around this issue without modifying my Lynx, but if you're not extremely careful it could damage the game or scratch up the console so try it at your own risk.