With fast-moving subjects auto-focus tends to let you down when you need it most, and with slow-moving subjects you don't really need it anyway, so if you assume you're going to be doing manual focus the teleconverter might not be a big problem. But yeah, check pro photo rental places in your area to see what it would cost to rent a serious long lens for the weekend.
I don't know about RC aircraft, but I know from shooting full-size prop planes you generally don't want a shutter speed higher than about 1/125, because when you go much higher you get frozen props in the photo rather than a nice blurred prop disk, which looks really weird (like the engines have shut down in flight). And yes, that means you have to be good with panning to get a clear shot of the aircraft. It may not be as big of a deal with much smaller aircraft, as the props may be spinning faster (considering the upper limit on prop speed is having the tips go supersonic, which is a function of both RPM and size) but it's something you may want to test before you're shooting "for real."
Although... 120" wingspan? Holy crap, that's getting into the "carrying Hellfires over Waziristan" range of RC aircraft.
With the relative angles, most of the time the planes aren't moving fast enough in the camera frame for autofocus to have a problem. However, for flybys where the camera is close to the runway and at a 90 deg angle, you are correct about autofocus. My D70s does a reasonable job in continuous focus mode most of the time. However the pan can be rather challenging as a plane traveling at 100mph, 75 ft away, moves really fast.
The problem is the same with RC planes, re: the prop disk. Usable shutter speeds really vary depending on the size of the prop and motor RPM. Landings and taxing can be in the 1/250 range to 1/2000 for a full throttle fly-by.
That image is a crop of a shot taken at 300mm f/5.6, 1/2000s. To give you an idea, that plane has an 80 inch wingspan and the props are probably about 10" in diameter, spinning at around 9000 rpm.
I'll have to look at the Sigmas. My immediate thought on the 50-500 was "jack of all trades, master of none". I just can't imagine a lens with that range being very good at any setting, but I'll go read. My normal lens rental place doesn't carry them, but I'll see if anyone in town does.