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Kiran:
I am not 100% sure about this, but you should not worry. I applied for my second EAD 2 months before expiration.
Did not receive approval or a card until one month after expiration. But the card was dated correctly - so the month that I thought I was not "covered", I was. I was not too worried because I have an H-1 as well (and I had received the Adv Parole within 2 weeks of the application!).
I believe it is enough that you apply in advance, which you have done - so the card will be dated accordingly.
Hope this helps...
KP