Ways to slow labor process?

So I am 38 weeks and 2 days. My doctors office STILL has not filled out my husbands FMLA paperwork and I’m kind of freaking out now. I didn’t realize it was was such a long process. I gave them his paperwork on 8/19, paid the “filing fee” and was told 2 to 3 weeks. Okay, kinda freaked me out a little bit but I didn’t want to bitch. Had I known it would take so long I would have been in my husbands butt about getting me it sooner. My last appt was on 9/5 and they said nope not yet, we will call you. I obviously go weekly now, and my next appt is on Tuesday 9/10.

But I’ve had a lot pieces of my mucus plug come the past 2 weeks. Was 2cm and 70% effaced at the appt on 9/5. And sorry for the tmi, but just had this.

Definitely bloody show right? What can I do to at least make sure I wait until Monday/Tuesday to raise hell to get the paperwork? I don’t want my husband screwed at work 😔☹️