Fans of Alternity

It does seem like faking pregnancy would be pretty easy for magical people. I'm sure you could do some convincing spells to give the appearance of various stages of pregnancy, and a married couple becoming pregnant is certainly not unusual enough for people to be checking your cover story too closely. And if even one St. Mungo's employee were in on the operation, the "pregnant" witch would be able to go into a room with him/her, make some baby-delivering type sounds, emerge with a baby looking tired and happy, and you would have a very tight cover story.

The scarcity of spaces in the program probably mostly has to do with the fact that there aren't that many wizarding families who can be trusted to be let in on the secret. I can imagine that it is very dangerous every time a new family is approached. Maybe Frank and Alice claim to be working alone (even disguised with polyjuice, perhaps) so that if they are ratted out, only they take the fall and the network can continue. Of course, this is why Neville hasn't heard from his parents for a long time: they are in the most constant danger of anyone, in this operation, and need to make sure that they are caught, their actions are not connected to their son.