You could make a Stabilitex overlay mount. Use an alphacellulose 4-ply mount board the size of the item; I suggest a reverse bevel cut. Paint acrylic medium or gel around the perimeter of the board's back and let it dry.
Position the item on the board, lay on the Stabilitex, and wrap it to the back of the board. Secure it to the acrylic medium by activating with heat.
Then float-mount each of the individually-mounted items to a common backing board in a pleasing arrangement. Put plenty of spacer under the glazing.
What did you mean by, "...I'm not sure if they would stay in place using mylar encapsulation"? Are you concerned about the item moving within the mount, or securing it to a board backer? Done right, the static, pinching action, and sheet pressure of a clear film mount will hold the item in place unless it is quite thick, textured, or heavy. In that case, clear film would not be a good choice. It's interesting that your customer complainted about the "look" of a clear film mount. Most customers like it. And most framers appreciate that it is easier than something like the Stabilitex mount described above.