Turns out Neville is a tosser too!
I found two chicks on the floor of their cage just now. Luckily they were both still alive and very squirmy so I think I found them in time. I immediately put them into Godric and Minerva's nest along with the three other eggs which hadn't hatched yet. I'm pretty sure only two of those eggs were fertile though.
Cross your fingers! It looks like it will work. Minerva flew right back into the nest and snuggled down so looks like she's okay with it. As long as Godric doesn't get upset it should be fine.
Send good finchy thoughts this way!