StillPatient,
The AC21 simply allows you to switch employers if your 485 has been pending for over 180 days as you rightly pointed out.
As far as getting an EAD and AP for you is concerned, I think I may need to agree with your attorney about the EAD for you. If you have well over a year left on your H1, why bother? The EAD has a validity of a year, and if it happens that you are still awaiting a decision on your 485 by this time next year, then yes, go ahead at that time and file for EAD. At the same time, it doesn't hurt to have an EAD if you intend to accept part time employment or take a second job or start a business or something right away.
The AP is not a hard and fast requirement, but its most needed for individuals who do not have a visa endorsement on their passport despite holding a valid visa status. It saves you the trouble of going to a consulate outside the country and getting your H1 stamped on your passport. If you currently have a valid visa stamped on your passport, you don't need AP right now...maybe next year if at all.
Lastly, I don't understand why you'd need your parents' birth certificates? All you need is your wife's birth certificate, and if that certificate is not in English, you would need to get it translated/transcribed. Talk to your attorney if this is the case, since they usually know certified translators. If not, just google for them, or do it yourself if you can. Parents' DOB and POB evidence is NOT required...at least no one asked for ours and I haven't heard anyone being asked for it.
Good luck!
ks