Just finished reading this thread. Lots of good info regarding how to remove a broken egg! Sorry that you ended up losing her! You did all you could.
I just had this exact some thing happen to a hen a few weeks ago. Thankfully she was not laying, but she had the same kind of crusty vent. It would not go away after weeks of treatment (soaking, nustock, antibiotic and wound ointment). Finally I realized it was FUNGAL and not an infection. I grabbed my Desanex anti fungal powder and dowsed her with that, out of desperation. After a day or two I saw HUGE improvement. Sadly though, she had the same problem as your hen, her vent healed too small, and she got constipated.
I just had this exact some thing happen to a hen a few weeks ago. Thankfully she was not laying, but she had the same kind of crusty vent. It would not go away after weeks of treatment (soaking, nustock, antibiotic and wound ointment). Finally I realized it was FUNGAL and not an infection. I grabbed my Desanex anti fungal powder and dowsed her with that, out of desperation. After a day or two I saw HUGE improvement. Sadly though, she had the same problem as your hen, her vent healed too small, and she got constipated.