More specific to the argument at hand, why should a debate about reliability of intuitions disqualify philosophy? Do you believe this is a settled debate? And if so, on what grounds is it settled?

The center of the issue is that you can't answer these questions empirically.

I'm not sure what you mean there. Didn't Luke just present empirical evidence that our intuitions do vary? That answers the question. Our intuitions vary, therefore any way of conducting philosophy based on assuming they don't is wrong.