Back to basics - at the shutter speeds used camera shake is unlikely to be the cause of the quite obvious unsharpness. All camera body instructions have a section on getting good results with AF - including a warning AF targets like the one you used can fool cameras into focusing inaccurately. The advice is also on the web http://nikoneurope-en.custhelp.com/app/answers/detail/a_id/4585 Digressing the individual sensors in the D7000 are larger than in the 2 FX bodies. This might be the reason the D7000 image is the least sharp. Why not try again using manual focus instead of AF? I agree there can be loss of image detail due to the high ISO and the atmosphere effects with a 7 mile distant subject, but the varying sharpness indicates AF failure is the most likely cause of the poor results.
Photography is a bit like archery. A technically better camera, lens or arrow may not hit the target as often as it could if the photographer or archer does not practice enough.