H1 transfer from company A to company C as company B is pending

My Company A is not doing good. I got offer from Company B and they have already got receipt(receipt date: Jan 3, 2018) for H1 COE/transfer in Regular Processing before last day(Jan 5, 2018) in company A. Company B has delayed start date by 3 weeeks (Jan 29, 2018) after my last date in Company A. Will the gap make me out of status ? Will new rule of 60 days grace period cover me ?

As Company B was delaying the start date, I got offer from more reputed Company C, they have initiated the H1B COE/transfer (Jan 17) as well based on company A H1 approval status in Premium Processing. The joining date of Company C is one month after start date of Company B, Can i legally start work for company B, then resign and join company C ?

Please let me know thoughts as I want to be safe, seeing the current situation going on ?