I have the same camera, and used to have the same lens.
Jan and CYKA both have good points. Spot metering may be fine on dark or colored planes, like Southwest, but will certainly overestimate the light source if a light-colored or white subject is being evaluated. I'd switch over to average metering, and only use spot metering if you have to shoot in poor weather. Remember that a camera's metering system assumes a certain light level is "proper exposure", which is typically 18% grey. A sun-lit, bright colored plane will certainly be lighter than this, and the camera compensates to reduce the light level.
Setting the speed priority forces the camera to vary aperture to get the desired exposure. At 300mm, your lens can only open up to f/5.6. 1/1000th at f/5.6 needs a LOT of light - your camera is probably wanting to go down to f/4.0 or even wider, but can't. Result = underexposure.
I had the same problem when I tried settings on speed priority. I ended up finding the widest f/stop I could use without the vignetting being too bad (f/6.3 or even f/8 on that lens), set it at that f/stop using aperture priority, and let the camera work out the speed. That means that you will be working down at the 1/250 range, but I think it's the only solution. LEARN TO PAN (hint: swivel from the waist, and try to overcome the natural tendancy to stop moving the moment you hit the shutter).
If you really need more speed, try the widest f/stop of 5.6, which will get you an extra half or full stop, but you might get some vignetting.
The only thing you should feel when shooting a terrorist: Recoil.