Induction questions

I was induced with both DS1 (induced at 38+5 due to pre eclampsia) and DS2 (induced at 38+5 due to waters breaking but no contractions after 18 hours) and when I was induced my cervix were already effaced and I had already dilated 3cm with DS1 and 3-4cm with DS2.

This time with DS3, I'm now 38+4 and as of Monday was only 1cm dilated and cervix only 60% effaced. OB said his head isn't engaged yet (but that's common for second and subsequent bubs).

Question is - because I never needed gel to soften my cervix and help dilate me with DS1 and DS2, will they still be able to induce me with DS3 if I'm only 1cm dilated, 60% effaced and his head not being engaged? I've heard that sometimes they don't like to induce when they're heads are high as it can put you at higher risk for cord prolapse (which is one of my risks according to my OB)?

Thanks in advance. I'm seeing my OB on Monday and planning to ask all these questions but just thought I'd see whether anyone else has been through something similar?

Things can change quite quickly, especially with subsequent children. do you need an induction again this time?