Well the 7DII supposedly AF's to f/8 according to the spec sheet, so yes it should work with the 100-400L + 1.4× Converter. How that will compare to either of the Sigma 150-600s or the Tamron is hard to say. From what I have read the 100-400 MKI can be very variable with converters. What the MKII will be like we will have to wait and see, although that will probably be a more expensive option than the Sigma Sport when you add the cost of lens and converter. You also need a 1 series or 5DIII (or already mentioned 7DII bodies to maintain AF. Sigma also suggest that the 150-600 Sport will work with the new Sigma 1.4× converter, while reporting aperture, while on a camera that will AF at f/8. This combination will then get you to 840mm.
Alan