I797 validity reduced - implications

Hi, Does USCIS reduce the validity of I797B in a new filing? . My previous employer I797 was valid till 2021 February. Now, I am joining a new employer and the attorney today mailed saying that I797 approval is till May 2020. This kind of lands me in trouble as my existing visa stamp is valid only till Sep 2019, and I was planning to go for restamping in June2020 after kids school closes. But if my I797 validity is only till 2020 May, I will need to go and get it stamped prior to it to file for extension right ? And even if I get it stamped now, they will stamp me only till May 2020, forcing me to travel again once the extension comes. My current I-94 is valid till 2021 February. Which one will take priority on employability I-94 or I-797 ?