I had played around with an idea for hanging two 5 gallon fuel scepters off the rear drip rail = just above the rear tire on the drivers side using two 'side mount jerry can holders' (link below), and then attaching 4 high load suction cups to the bottom of the back panel plates (outer 2 corners)...I didn't want to drill any holes in the side of my van without access for a backing plate of sorts (I have no access either).
Same principle may work for you...I didn't proceed simply because I was sceptical when considering how secure it would be carrying 80lbs of fuel on a bumpy backroad. I could see the same principal working for 18lbs of traction boards though.
Here is the link for the racks that would hang from the drip rail (I was going to 'join' them by attaching a 1/4"thick x 3" wide x 24" long aluminum plate towards the bottom end and positioned between the two - so they would be secured together & to keep them from swinging.
You need to envision these racks without the sides and front which are intended for securing the fuel cans:
Then I was going to mount the suction cups to the bottom of the rack at each corner (placed so when the cans are in the rack you wouldn't see the suction cups):
You could easily make a similar hanging drip rail rack on your own that you could mount your Yakima's to. This would keep you from drilling holes, and would be easily removable.
Just sharing an idea.