I find centre spot focus a real challenge with bird-in-filght, especially with my main lens, the very heavy 150-450mm.
So I have reverted to zone-select medium. AF-C.
And, with the huge 150-450mm, continuous shooting (medium or high).
And finally, a shutter speed of 1/2000th. If your tracking skills are better than mine, you might be able to get away with a slower shutter speed.
I presume the 300mm will make tracking easier.
Here is a recent shot of mine that I was pleased with using my 55-300mm PLM lens:
Long-billed Corella in Flight - PentaxForums.com
And one with the 150-450mm monster (note the higher shutter speed!)
Pied Cormorant - on Landing Approach - PentaxForums.com.
Generally, unless you are up very close and personal, you don't need to shut down for depth of field, because of the distance between you and the subject, so you can stay fairly wide open with the aperture, and go for shutter speed.
I have saved my preferred settings to one of my custom User settings.
The 150-450mm zoom has 3 distance settings to minimise auto-focus time and hunting: near distance (2-6 metres), full range, and a 6 metres to inifinity. I don't know if your 300mm lens has any equivalent.