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Hello, Bob, dioramas aren't my thing. For wargaming WW2, the issue is to be able to move the plane, so I put up with a stand that is not "invisible".
http://www.tigerterrain.com/1100-ww2-planes.html
Scroll down to the Spitfire: I've scratchbuilt this type of thing using coathanger wire, painted green. Having a sturdy base that *won't* easily allow the plane to tip - disaster- is important. I use terrained hard wood.
Some people need their planes to dive or climb and use telescoping aerial. See:
https://s43.photobucket.com/user/Top_Gun_Ace/Topgun%2520Marketing%2520Flight%2520Stands/story
These are very visible, of course.
Now your problem is different. Invisibility is the key. If your diorama has a roof, it would be easy to suspend the model using fishing line. Otherwise, a solution, not unlike mine (above) using clear perspex rods is about the only answer.