Mudman not being an expert but using the same camera and sigma lens,150-500 your settings should give you good results,the first thing that I noticed was purple fringing in the lower branches,it is not motion blur,this is from high contrast scenes.

The settings I use are spot metering,natural,AV,this gives me different shutter speeds but quite often 120+aperture 6.5, all of my photos are at iso 100-400 the lower the better,and all hand held.

Would you be able to shoot the same scene at a different time of the day as there is a lot of shadows and direct sun in the tree.

Jack.