The D7000 will actually focus at f/8 but it requires good light. Nikon is conservative and the reported limits are for reliable AF.
One clarification - the reported focus is usually for a lens wide open regardless of what aperture is selected. Most cameras will provide a wide open view through the viewfinder and you use the DOF preview button to see how it really looks. So a 2x converter on an f/4 lens is f/8 wide open - which is borderline on the D7000. Even if you chose f/11 for your aperture setting, the combination is f/8 wide open and should focus with good light and a good subject. My experience is when it comes to AF the center sensor is better than the surrounding sensors - and much better than the outer sensors. Darrel Young has documented that for the D800 and I expect it is the same for the D7000.
The Nikon 300 f/4 provides better image quality than the Sigma 150-500 even with teleconverters. The bare lens is clearly better, and nearly as good with the 1.4 teleconverter. With the 1.7 lens you have an effective 510mm - borderline on the Nikon but at the point where the Sigma zoom is losing quality as well so the Nikon is still as good or better (in my opinion
).