Hens go broody when you don’t want them to… and won’t go broody when you do. 
It is winter (here at least, not sure where you are). My two and 3 year olds haven't started laying yet for the year. Vent gleet is fungal (yeast). If the antibiotics help for a spell and then the issue comes back, then maybe the antibiotics aren't fully clearing whatever bacterial infection they have and it is salpingitis, but 3/12 is a really high proportion of 2 year olds to have salpingitis and maybe it just comes back to the stock source.
