Sorry, I am having a bit of trouble with this.

First of all what does "contingently necessary" mean? Perhaps I am showing my ignorance, but the two words seem contradictory.

Second, you say "... under the principles of science consciousness... necessarily cannot affect matter at all."  What principles of science are you thinking of?

Third, I thought it might be an open question of whether and in what way conscious experience can influence matter.  Why do you say consciousness "necessarily" cannot influence matter?

I take your point about memory of what happened under anaesthesia. But in my case I was not under anaesthesia.  I was under a drug that impairs memory.  I assume that the neurological effects are different.