knowing where to stop could easily be a challenge with the method you nominate.
You would be thicknessing the entire door without ready access to the remaining thickness of each face of veneer.
I think a better method would be to saw the veneer, temporarily attach it to a MDF carrier and thickness it to a consistent 1/8" or 5/32", or so.
build the door and attach the veneer skins. Then sand the final construction.
When gluing on the skins, you may wish to consider using epoxy thickened with wood flour. With the "right" choice of hardener (and storage post mixing) you should be able to achieve an open time in excess of 60 minutes. For example, SystemThree's general purpose epoxy with SystemThree's slow hardener has an open time of around 1 hour at 75 degrees.