I have a Sigma 300mm f4 Tele macro which can be found here:BTW, which 300mm do you have? I use the Sigma TC's with my 120-300/2.8 to good effect... a lot cheaper than a new lens...
Do you have DX or FX? 300 mm on DX is about 450mm equivalent. A lens that goes all the way to 600 mm (900 mm equivalent) may be tricky for aviation photography as I struggle with longer lenses pointing the camera the wrong way during displays...
I have heard good things about the 200-500 mm lens, cashback is available at the moment.
But one thing isn't clear - budget! no point us advising you to pay £1200 or more if your limit is £200....
The Nikon 200-500mm f/5.6 is fine on a D500 (and D7200 also) for aviation work, light enough to handhold for extended periods.
GC
How about a sigma 150-500 then if you don't want to break the bank
I would just put a sigma 1.4x on it and see how it fares... If that's not enough, then you're really looking at 600mm+ options...I have a Sigma 300mm f4 Tele macro which can be found here