OPT Expires on January 29,2018 and I want to apply for H1B Visa on April 1st.

My OPT expires on January 29, 2018, and my employer is willing to finance my H1B application on April 1, 2018.

Counting the 60 days grace period after my OPT expiration(01/29), I would need to leave the country on March 30, 2018, which is exactly 2 days before the H1B application (4/01).

Am I the unluckiest person on OPT, or is there ANYTHING I can do to bridge this 2 days gap that would allow me to apply and wait peacefully in the US for the results of the application?

Please help me out if you have any experience to share/ advice to give me.

Thank You!