FEHB transition without insurance gap?

I am on DRP and received an offer of employment in the private sector. My family is currently on FEHB through me, with the premiums taken out of my paycheck. I'm not sure if I can stay on DRP with my new employer because of ethics rules but I don't want a gap in my health insurance coverage.   My new employer can only begin my insurance on the 1st of the month following my employment, so I either need to start before Sept 1 or Oct 1 but, if I have to resign my fed employment before I start I think it means I'll have a day or 2 gap where I can no coverage. Is that right? Or does your coverage depend on pay date i.e. if 8/29 is the EFT date and 9/3 if the official pay date, I'd be covered under FEHB until 9.3 since I already paid for the premium from my previous paycheck? If not, what have people done to cover a short gap?

Trying to get someone in my agency HR to answer this is going to be a nightmare given that they are in the middle of a reorg and many have taken DRP..... So I am trying to crowdsource and see what others have done.