Best Bike Rack for Honda Pilot?
Most of the less expensive car/van rear racks are shaped like this:
 

The arms with pads rest against the vehicle and then straps from the center attach to the hatch, trunk and/or bumper.  This should work if you attach the straps to the top, bottom and if included to the side of the hatch.

You would be able to open the hatch if the bikes are removed first, but it is likely that the hydraulic hatch struts will not keep the door open with the added weight of the rack.  If the bikes are on the rack the weight will be significant and you will likely have difficulty opening the door.

For a rear rack at allows you to easily open the door and still keep the bikes stored I think your only real option is a hitch rack.