hi there... so sorry to hear about your 1st son.. must be a difficult time for you right now. Regarding induction i don't think babies head has to be engaged.
My advice regarding induction is just be prepared for it to take a while to work... i was induced with my first daughter when i was 7 days overdue.. it actually took 2 full days to get me dilating at all and then they broke my waters, put me on the drip and she was born 13 hours later at 10 days overdue (i went in to be induced on the thursday and she was born on the sunday). Although this might not be the case with everyone i had just never heard of it taking that long and nor had my family so they all worried etc!!
Although many people have terrible stories to tell about induction mine was absolutely fine and one of the best experiences of my life so try not to worry too much... i had an epidural and a "natural" (if it is still called that with induction!) delivery. Took just over an hour for the pushing stage.
Compared with the extremely fast and painful birth of my 2nd daughter I would choose a slow, controlled, induced labour again without a doubt!!!!
Why don't you check with your midwife and see if she can find out why they didn't give you a date? I hope you find out soon x x x