Thanks, 863211 and schweine_srq. I talked to a couple of attorneys. One of them told me that if I applied for cap-exempt H-1B, which would allow me to extend my stay from June to Sept. Because I remained legal status before Oct. 1, I was able to file change of status within the US.
In addition, because the Oct. 1 H-1B does not have an I-94 with it, my status has not been changed to H-1B. Therefore,Last Action Rule would not apply to this cap-subject H-1B if I applied for a cap-exempt H-1B. It is consistent with what 863211 said, the cap-subject Oct. 1 H-1B is still valid.
Teacher 863211 or any people who has experience with it, pleasse let me know if the information is correct. I am in a tough situation, I really need to think carefully before any move. I will appreciate any of your advice!