You can claim the sleeping are in some way conscious, but in a vegetative body, one which has no alpha waves, and which we would therefore declare brain dead, all of the machinery you allude to is still active and generally not compromised.   It also has all that history.  So no part of this explains consciousness.  If I return the body to a functioning state, consciousness may or may not return, and that consciousness may or may not see itself as a continuation of the previous consciousness.

Since consciousness can cease or resume for reasons unrelated to protein and nucleic acid configurations (say brain trauma, overcome by neuroplasticity), looking back across generations does not reduce out whatever other factors are needed for consciousness, so that lead is a red herring.

The direction we need to look to find whatever information is necessary for consciousness must include spreading outward in the present as well as, or instead of, back in time.  I would vote for 'instead of', on the basis of a common science-fiction thought-experiment.

If I constructed a functioning body identical to my own, I may or may not be able to capture everything that maintains my consciousness in the duplication process.  But if the copy is exact enough, it is likely we can give that body what it needs to become conscious in some limited sense.

So I would argue that no part of my biological history is truly necessary, only imitation of some aspect of the present state.  Though, as the brain-death example shows, those aspects of the present state must involve something more than my nucleotide and amino-acid configuration.