Is there any such thing as a rectangular tripod mount or something like that?
Pro tip when hardware hacking: When you have to work this hard, yer doin it wrong. 

Get two mesh pouches - like laundry bag but the size of a cell phone / external HDD.  Make sure they have draw strings you can velcro or knot shut. 

Get a rectangular plate of thick mylar or thin aluminum sheet somewhat smaller than the HDD.  Put it inside the pouch.  

Attach the plate to the bottom of the laptop tray with pop rivets or epoxy.   If glued, scuff-sand all flat surfaces.  This will trap the upper part of the pouch between laptop tray and plate. Free the lower part of the pouch from the rivets.

Put HDDs inside pouches, cords coming through opening.  Draw string/velcro to secure.