A typical deer shoulder mount is much lighter than most think. Your LL might be thinking it will take a huge bolt to anchor it to the wall(??) Heck some of mine are hung on average sized wood screws only into the sheetrock. That said, if you simply want to do as they insist I'd suggest something like this; a 12"+ diameter log split in half. I'd suggest a length of 18" to 2 feet for this base. Using the flat side as a base bottom, use (as already suggested) a metal rod or metal strip bolted to the back of the plaque. Using some trial and error bend it at an angle that will tilt the mount & plaque a bit rearward. Find a piece of a tree branch or small tree of 3-5" in diameter and 4-6" (or more?) in length. Drill a hole through the limb top to bottom (lengthwise) big enough to thread/fit the metal rod (strip) through.
Drill a hole into the curved top of your split log/base and epoxy the rod at the proper angle to hold the rod straight up out of the base and have it bent so to hold the plaque at the desired angle. This bend/angle would be right where the bottom of the plaque is. Then, adjust the overall lenth of your branch (with drilled hole) so as to be proper length to hide the metal rod between the plaque and base. Should be pretty natural looking and very inexpensive to make.
Good Luck!