URGENT - Pls Advise. H1B Visa Transfer (Job Termination Case)

My last working day was 10/Mar/2018. Grace period is until 7/May/208. My H1B started on 10/Jun/2015 and current extension is till 01/2019 with I94 until 04/2019. Now I got a job offer with New Company A who is filling my H1B Transfer this week and I have not yet started my job with A. I m expecting a better offer from New Company B, which I am interested for - however by the time I receive filed H1B Receipt by Company B, it may cross 7/May. So, Do I have to join Company A, just to activate my H1B filed by Company A, OR I can simply wait till Company B to file and send me H1B receipt and I start working at Company B (pass Company A & not join at all ) - PLEASE ADVISE.Also, Can I start working with the Receipt or full approval is required?

Also is it possible that, when I receive the approval from Employer A or even Employer B, USCIS may give a an Approval with out updated I94, by which I will have to go to India to get is stamped? PLEASE ADVISE - Thanks.