You may get different answers regarding this issue. I believe the confusion is due to INS/USCIS whatever's ambiguity on this issue for a few times. My lawyer told me recently to refer to the Cronin Memo, which was published in May 2000. I recommend you do some search and research, and maybe you can post your opion.
My understanding is that one can either use a valid H visa or AP to enter, and the decision will result in different status after the entry. I feel my best choice should be using AP to enter, and continue work legally without using my EAD, and apply for H extension, so the status will be switched back to H non-immigration. This will keep my H & pending I485 backup alive.
There are still some concerns like, whether the Cornin Memo reflects the final rule or not, and what are the details for applying for H extension with an parole I-94. Maybe you my friend can complete the research.