Updating is indeed an important process - the model must be kept up to date to be of any use - but the process is not conscious, it happens automatically. No?
Yes, we can stop the visual updating by stabilising the eyes or fixating as you say in your first point (or simply by closing our eyes :).
What is this "we", commonly known by the admittedly slippery term "self"?
a substantive quibble sounds oxymoronic but much of life is like that I think; so much depends on context and view point.
My reasons for asserting the "updating" as central:
* awareness is a process or [suite or 'cloud' of] processes involving real changes. This is shown by the fact that if the process of perception is constrained, eg by holding the eye still, or holding the sensing body part still, or holding the attention on one object, the perception stops and the object/subject in focus slips out of awareness. Something similar happens when the stilling of focus is purely internal.
[Why this happens, could occupy us for half a lifetime, so ignore it for now]
* the "self" is not definable except in contrast to and relationship with "not-self" so both, as concepts and practical reality, are moving targets [or movable feasts to a more optimistic mind set]; the world does not stand still and neither do people - with trivial exceptions noted of course - so change and dealing with novelty is most of what it is all about
* the corollary of this, it seems to me, is that the activity of the brain is aimed at assimilating that which is dependable and predictable - the invariances as many people call them - so that deviations from the norm can be dealt with as quickly and effectively as possible. Detecting and dealing with novelties entails prediction and comparison of before and after wherever necessary, and this is the essence of consciousness.