Here are the steps I am contemplating:
1. My spouse has an L1. So, that makes me eligible for an i539 (for L2) or an L2 VISA from the home country.
2. I would like to stick around in the US till end of August / beginning of July for an event i.e.a couple of weeks beyond my grace ends.
3. The only way to do that, (I am thinking aloud here), is to first apply for an i539. That will allow me to stay till I get a decision.
4. Concurrently, I apply for L2 VISA from home country. Travel to home country, and then get my L2S on entry. That way, I can stay for longer than my grace period AND get work authorisation too.
5. I can forget about the green card process for now.
thoughts?