Oh my goodness...not that my goodness has much ado about all this...
One way of explaining the way in which I am using the expression 'chasing windmills' (mixed metaphor or not, used correctly or not) is...I have something right in front of me (the painting) but at the same time, it is just out of reach (since I can't find anything about the artist named che), hence I am constantly chasing che (but since it's a portrait of Don Quixote) I feel it is more appropriate to use the expression 'chasing windmills' (see the connection?)...in my case I am not chasing rainbows. The expression tilting at windmills is used in the story of Don Quixote as a way of saying Don Quixote was tilting/jousting (attacking) the windmills he thought were giant enemies. I, on the other hand, do not have visions of grandeur (Don Quixote did) nor am I attacking anything! I am simply chasing windmills! Right or wrong, proper or not, I don't much care...it suits me just fine and conveys my quest!