I think the em-10 is probably the limiting factor! It has been mentioned many many times that Panasonic af is snappier than Oly, in particular with Pana lens.
Nah contrast detect and things that move just brings in trouble. Same issues with my panasonic GX7. that one is very very snappy even in low-light.
The DFD system of the GH4 might help but that's a big and expensive camera. You pay a lot for the video features. Which would be wasted money if your only interested in stills.
With airshows just manual focus and keep it locked at infinity. F6.3-7 at infinity will get all planes in focus sinc they are far enough away anyway.
With AF your camera will lose the plane and start hunting.