I understand your worry.
It most probably seems that the baby is drinking a lot of amniotic fluid
. This is not worrisome unless it causes other effects like fetal distress
I do not see a reason as to why you should wait until the next 3 weeks. If all is fine, you can be induced at 37 weeks when the fetal lung matures too.
Please discuss about this with your doctor.
Prolapsed cord causes more harm to the baby.
Hope this helps.