H1b Transfer: Travel to India for stamping Question

Hello All-

First off, thanks to this community for helping out with Visa questions in the past.

My latest question is relating to Travel to India for H1b Stamping.

I work for firm A where in i have submitted my resignation and my last working day is 16th Sep. I was hired by firm B with H1b transfer approved and the H1b start date per i797A is 5th Sep.

Situation: I wish to travel to India on 6th Sep. I will be booking a Stamping appointment for 7/8th Sep using the Firm B’s petition and plan to return on 15th Sep. My official start date with Firm B is 17th Sep.

Question: At POE, will i have an issue with the Firm B visa stamped on my passport since technically i am entering USA while still being employed by Firm A?? Please advise.

Additionally, do you think with 7th Sep Visa appointment- i will be able to get my passport back (Visa issued and passport available for pickup before travel date?) for my travel on 16th Sep? Or is this a hopeless dream on India visit that i am planning for?