If you have a very good lawyer and a very nice employer, maybe you can.
1. Prepare for PERM (should not be EB3) to get LC, try to finish it in 5 month. It's possible if the lawyer and the employer can cooperate. Especially if you had advertisement done already.
2. When you're waiting for PERM, prepare for I140&485 first. Once you get LC approved, file them immediately.
3. When you're waiting for PERM, prepare for 7th H1B renew first. Once I485 filed, file it immediately.
Reason:
H1ber can extend their H1b to 7th year if their I485 is pending.
I'm on the same boat, but I can't find a nice employer. So I have to give up. Good luck to you.