For some models, try simply fitting the LEDs into place. This may work well for things light vehicle headlights, lamps, and fire sources such a burning pyre.
Model Car Headlights
Some scale model die-cast cars feature translucent headlights. You can usually open these up by prying the plastic chassis from the body.
NOTE: a car with a metal chassis will interfere with the induction.
There is enough room here to place one LED per headlight, perfect!
A glue dot or other two-sided, transparent, squishy adhesive material is perfect for attaching LEDs.
Cut a small piece of the adhesive, then press the LED to it and peel off.
Press the LED into the backside of the headlight, or onto the plastic above it -- the plastic will act as a light pipe, allowing the light to shine through.
The advantage to this orientation is that it keeps the coil on the same plane as a floor-mounted induction coil for best power transfer.
You can try different materials to diffuse the light coming from the LEDs, such as wax paper, batting/cotton balls, hot glue sticks, and even the tops of conventional through hole LEDs.