My usual solution is to use a fixture cut for the part to fit into, then adhesive it in. (see, recently, Polyhedral Brass Dice Set and one of mine from the past A twisted little project ) Essentially, you pocket the negative of the first side to locate and support the part. I use an acrylic backerless adhesive, but many people prefer CA.
For a prop, you can also use the center hole for positioning and holding. A through hole affords a screw, and a non-through hole affords a pin, into the wasteboard.
A could say more if I could open the model. Putting images into you message makes things much easier.