Answer...
you can also try to get the stamping done while you are at your home country.
However answering your question,One follows another. That is if you have EAD and you USE it then the next time you travel you SHOULD use AP. By using EAD , you have invalidated your H1.
However, if you use AP to enter (and not used EAD before) then you CAN start using EAD afer coming back. However, H1 is not invalidated by AP usage alone. If you are with your sponsoring company and you get a valid H1 stamp (St.Louis or visit to canada) you need not go to EAD.
The whole premise is based on the fact that status is recorded by your employer and needs to be sent to INS only when asked for. Talk with your employer and lawyer as to how are you going to get the H1 stamp after coming in AP (or if they also agree with you in getting teh H1 stamp). This is crucial because by switching to EAD you might be saving your employer some money when they file H1 for somebody else.