I feel that for subjectivists and physcialists to have common dialog at all on the subject, we need a simpler definition of "consciousness" that is not implicitly biased against either camp, but based on real observation of real experience. Definitions by internal self-observation are biased to the extent they are not subject to direct self-report.
What we report happening as we feel time pass is the memory of time passing, and the evolution of all other memories seems to arise from references back to those memories of time passing.
So my provisional definition of 'conscious thought' is 'the memory of forming new memories'. It seems to me that we remember moments, and then discard them, and that we do not experience them until at least a temporary memory has been recorded. (More detailed argument here: https://philosophy.stackexchange.com/a/19596/9166 )
But it admits dreaming as a form of conscious experience. How much is that at odds with various people's expressed ordinary experience and previous philosophical consideration of the subject?
For example, writers consistently use sleeping as the example of living and unconscious. But do we mean to include dreaming when we do so?
There is also a perspective from which what is original about human thought is abstraction, which originates as a form of dreaming while awake. The idea is that animals generally do not abstract because they are either never (in waking time) or always (in dreaming time) composing alternative interpretations, and abstraction is the habit of composing stories about real life. (Rather questionable motivation here: https://philosophy.stackexchange.com/a/18484/9166 ).
(I guess that is presuming a modern interpretation of what dreaming is -- composing alternative interpretations of random neuronal firings until something apparently meaningful enough to seem worth remembering converges.)
So purposely omitting dreaming from our model of consciousness could be losing value and a warping perspective.