Refining that big picture and beginning to focus on the bird which is, indeed, the focus of the carving.
A new grip:
We've used to wood grain (fibres) to maximise the strength of the design. Nevertheless, at the end of the day this is a fairly delicate carving and as elements like the twig get thinner and we must work a 'softly, softly' approach.
Normally, I advocate against a 'backhanded grip', preferring what I call low or high angle grips but here is a case where working with a 'back hand' can help: there are fingers left over to support the back of the carving.