H1B effective Date when currently on L1B

Hi All, I am currently on my L1B and I am in the US. However, I have my H1B approved with Consular processing. I am planning to go for amendment on my approved H1B visa for a change of status. Is it possible for me to mention any effective start date. My current organization (L1B) is not ready to leave me until Jan 31.

What is the best approach to leverage my H1B without going back to India. Please advise. Thank you

You can request a specific start date however it is not guaranteed that USCIS will honor it.