Thanks a lot for your inputs and for directing me to the correct link. I have couple of follow up questions though:
When should I stop working on my H1b, is it as soon as I file the H1b to L2 change of status application? Or is it from the day my L2 gets approved (date on new I-94) till my EAD comes through?
Can I file for the L2 EAD at the same time as I file my i-539 form?
If I want to switch back to a H1b at some later date, will my application still be cap exempt or will I again fall under the cap for the year I'm applying for?