One path toward a non-materialist answer might be phrased in questions like, "Once created by, or emerged from, brain activity, in what way does consciousness continue to keep and express its purported physical origins and functions?
Does it in fact 'behave' in the same way as matter - or even the same way as the brain - behaves?
For example, vapor released from warming ice is 'liberated' from the constraints of solidity, and it takes on new properties and a new 'life' of its own quite separate from ice. Perhaps a similar comparison can be made to consciousness once it has been 'projected' out of its material matrix; in which case it is possible that, like ice-released vapor, consciousness has a seperate being and category level than the matter from which it supposedly originated".
I don't think you understand what is meant by "emergence" when it is said consciousness is an "emergent property" of a brain. That is not to say consciousness in some way becomes independent of a brain, ever becoming "liberated from its constraints".
"Emergent properties" or "emergence" refer to those properties that arise from the collaborative functioning of a system, but do not belong to any one part of that system. In other words, emergent properties are properties of a group that are not possible when any of the individual elements of that group act alone.
Current scientific indications suggest consciousness to be an emergent property of a brain. If consciousness is "projected out of its material matrix" as you say, then it should continue to function even if the brain is damaged, shuts down or is destroyed.
The problem is, there is no evidence to suggest consciousness is ever projected in such a way and can persist with normal function in the event of brain damage or destruction. In fact, there is no indication of consciousness existing absent a brain in any case.
But a more pertinent question might be - considering that Dharma Wheel is a Buddhist site - "What did Shakyamuni say about consciousness? And what do the Theravadan, Mahayanist, Vajrayanist, and Shin schools say? To what extent does Buddhist consciousness-experience, philosophy, and theory/speculation support, agree with, confirm ... OR conflict with and contradict ... the modern materialist point of view?"
I've studied Yogācāra philosophy in depth for years which goes into great detail on the topic of consciousness, in all its supposed layers. However, if it ever suggests any connection to a brain it says that the brain, as a physical aggregate, is a production of consciousness, not vice-versa. Or more precisely, it is consciousness itself, physical aggregates merely being layers of consciousness.
I'm not aware of Śākyamuni ever talking about the brain, and I wouldn't expect him to.