Nest Building

As I reported a few days ago, the magpies have returned to the nest they built last year, but they are adding significantly to the construction, bringing in new twigs every day and weaving them into the structure.  It has to be said that they didn't do a very good job last year (I had the impression it was the first time they had built a nest) so the improvements will,  I am sure, be very welcome.

This picture isn't very sharp.  The dark plumage of the magpies does mean I have to bring up the shadows quite a bit, and the high ISO probably doesn't help.  But even with the stunning follow focus capability of my camera and a high shutter speed, I'm still not getting it tack sharp.  I am wondering whether the image stabilisation (in lens and in body) is fighting the camera tracking movement.  Switching off the stabilisation doesn't help (unless I really increase the shutter speed, but that would mean increasing the ISO even further) and switching to Mode 2 (only vertical stabilisation, allowing horizontal panning) isn't a total solution as the birds move vertically as well as horizontally. Can any other bird photographers comment or give advice?