I think you may end up having to modify either the Light Jet or the head of the base to hold the Light Jet itself. When I mean modify the Light Jet, I mean cutting into it to allow for the base to connect. The drawback to this is that you'd be damaging the item. The other option, modifying the base, would be more challenging, That means you attaching something to the top of that base that would allow the Light Jet to sit balanced on it. A good example is what my dad and I did with a U.S.S. Enterprise-D toy by Playmates that I got as a part of an auction. Now, I already had one, but this other one we got, wed decided to use as a display piece. My dad had, at the time, had cannibalized a gaming joystick from Logitech to use the inner electronics for a MAME cabinet he's working on.

Anyways, he had the base and the inside stick left over with the intention of throwing it away. After some discussion on how to display the Enterprise, I jokingly said, "Too bad we can't recycle the left over pieces of that joystick. It looks almost futuristic to be a base." After a moment, he agreed with me and we ended up modifying it so that the base could hold the front heavy toy. We then took a piece of plexiglass, cut it the size of the battery compartment so we could slide it into the battery compartment without damaging the toy. Right now, it sits on my display case and it is still holding up.

So, those are the two options you got, either to modify the toy or modify the base.