36 weeks and no thinning/dilation at all 😫

Just received a cervix check today at 36 weeks and it’s been determined that baby is head down, although still very high- cervix is still closer and hard. Doctor recommended sex, to help thin the cervix but any other advice? Obviously I know baby comes when baby’s ready, but she says if I’m not at least 3cm within the next 3 weeks, I’ll be doing a 3-day induction, which sounds treacherous, granted we add another 24-48 hours of monitoring afterwards for a total of 5 days in the hospital. 😭 the goal is to labor naturally

Update: I have GD and preeclampsia, therefore they are not recommending I go past 38 weeks, which is the reason for the urgency.