"Excuse me!" he calls through the door. "I'm a miracle distributor from another world and I'm here to save your children from mysterious dragon baby death! I can also turn the red one into a unique in the process, but I've been advised not to do that with green-groups for safety reasons!"
"I'm a miracle distributor from another world and I can use otherworldly magic to avert mysterious dragon baby death. Both of your children have the problem that causes it, and I would like to fix that."
"Okay. It happens not to cost me any extra magic to turn babies into uniques when I fix them, but I've been told that making more green-group uniques is a bad idea so I'm not going to do that with your green-group child, and red-group uniques seem to sneeze fire an awful lot so you might not want me to do it with this one either. I'll leave that choice up to you."
It occurs to him that he's not sure where dragon magic comes from, or where it goes when it goes away, and that if an eight can come up with a unique's worth of it every time, there's no saying he can't just put part of that into a baby dragon and let the rest... do whatever extra dragon magic usually does.
He tries it with the malachite first: an unusual's worth into the baby, and the remainder of the magic the coin is capable of generating just—spilled.
"All fixed! Have a nice day!" he says, and moves on.
It takes a while, but he does get to all of them. When the next teleport fails, he teleports to whichever unoccupied parked lift is closest to the headmaster's office in the Very Beige Institution, and pauses to see if Keo is still there.
In that case, he asks the lift to take him to said office. (This seems politer than just teleporting directly into it unannounced.)
"Oh, hello," he says. "That's interesting. I finished fixing all the doomed babies! I didn't make any green-group uniques, but lots of unusuals, and plenty of uniques in the other groups. You might have to find a new word."
"That," he says, with a gesture that takes in Keo and her elf. "Your mind... thingy. I saw it earlier but I wasn't really paying attention and didn't pick up on the details; it's much clearer with both of you in the room."
"That... is a depressing statistic," says Lazarus, blinking. "You're welcome. I - hmm - I forgot to keep track of the time, oh dear. Do you happen to know both what time it is now and what time it was when I first talked to you?"
And back to where he left the miracle couple on the bottom of the world.
The single-minded purposeful energy that carried him through the un-dooming of almost three hundred babies has begun to fade. He could go track down Kaylo again, and ask him strange questions about the draconic aging lack-of-process. Or he could go track down Libby and find out what arrangements she's making for housing the three of them while they wait for Milliways.
He does the second thing.