OK, rabid homo-erottic babble aside
you could try doing one of the battery mods and change the connections over to the snap type, you'd need two connectors which are about 40p a time from maplin. the bonus here is that due to the size of the snap connector the batterys will hold in the hopper without the need for a door.
If you're really stuck and as the egg2 isn't that hard on batteries you could try sticking the door with a tiny blob of superglue, enough to hold thing in place, but also not so much that you can never get the door open again.
what they refer to as 'tacking' in the welding world...