H1
I'm not a lawyer, but i think it is a simple question.
Big question:
Are you working on H1 or on EAD now?
If you are working on EAD, you MUST travel on AP.
If you are working on H1, you CAN travel on AP, but i'd rather you travel on H1. First of all, if you work on H1 and travel on AP, you'll have to give your HR your EAD and redo the I-9, as your status now changes from H1 to Immigrant. Second . . . Imagine your I-485 is denied. 99.9999999 it's not going to happen. So, relax. But sometimes there might be technical errors, INS screw-ups, etc. you just never know 100%. As far as I understand, if you are still in H1 status and your I-485 gets denied you are not really in any trouble. But if you lost your H1 status you could be.
So, travel on H1 if you haven't lost your H1 status yet.