".... those who espouse a material-only view of consciousness often resort to notions of complexity to cover the fact that they are leaving out the inexplicable bits and the "ruled-out" phenomena."

Maybe so for some, but the scientific approach is to be agnostic about the inexplicable, and not to have 'ruled out' phenomena.

There have been many past attempts to draw a line and say that such-and-such a phenomenon can only be produced by living or conscious beings. Animal electricity and organic chemistry jump to mind. The fact that those notions were mistaken does not mean that any currently unexplained phenomenon must also ultimately prove to be material in origin; but anyone proposing alternatives to matter-and-energy have the duties of tentatively describing its properties, and of suggesting ways in which the hypothesis could be tested.

And nobody should reject an idea merely because the consequences are uncomfortable to them. The only criterion for acceptability is the robustness of the idea under objective testing.