I didn't even know it was in the contacts list. Still, if it's there you can work with it. Have some "action" that transports an anti-matter warhead (or something equally nasty) into the doomsday waffle cone and then have it dissapear with a bunch of explosions and debris in attendance. You can't fight it the way you can in the Cryptic mission but hey...
Place an invisible object (the biggest one) on the map. Place the Doomsday Machine npc on top of that object. Now place one or more explosion details right on top of your Doomsday Machine.
In the "states" tab for the explosions, set them to go from invisible to visible on "component complete" and target that at the invisible object. Then in the states tab on the Doomsday Machine, set it to go from visible to invisible on the same component complete.
This way, the machine will seem to explode when you interact with the invisible object. Select the invisible object and in the "triggers" tab you'll be able to set an animation and what appears on the interact button. I would also, using the states tab, set that invisible box to only become visible when you want it to.
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You could place an enemy group, and change their costumes to the Doomsday machine. The only problem with that is it wouldn't use it's antiproton beam like in "The Doomsday Device" mission but it would be able to fight the player and get destroyed in the end.