If aperture is important,. then you have your lens in the Sigma 120-300mm.. and the option to get perfectly useable results at 240-600mm f/5.6 when light is plentifull but need more range. (or when ISO noise can make up the difference in light loss)
However.. Ihave noticed over the years that since "superior" image qaulity and performance is not the usual top requirement for this type of shooting,. that detectives and paparatzi often use the lower cost slower aperture Sigma zooms that we wildlife and sprots shooters tend to avoid. The Sigma 135-400mm and 170-500mm for instance,. and of course the well liked "Bigma" 50-500mm of higher quality.
They must just use super high ASA film in these rigs.. (you can allways see horrific grain in these shots) to make up for some of the light loss.
In between there's the 100-300mm f/4 EX from Sigma,.. if F/4 is fast enough this would save considerably on $$ and weight.