Hi @bs2019
As per the law, everything should be done by 60th day. Rest is your choice if you want to still stay and do things after 60th day.
As per my information, USCIS receipt number should be generated by 60th day to prove that you got into H1B status within 60 days of grace period.
I do not suggest to rely on Fedex delivery date. USCIS will not honor it later. They only consider their own receipt date.