Thank you for an interesting and thought-provoking essay. To me it's clear that thoughts are brain states. So, based on your essay, I agree with Paul Churchland's position. We must distinguish the content of the thought from its location. And we must distinguish both of those from the object of the thought.

For example, take the number Pi. It does not "exist" as a number separately from our thoughts about it. It's true that if we measure the rations of circumferences of circular objects to their diameters, we find them to be approximately the same. And mathematicians have defined Pi as a number to correspond to that approximation.

But the number Pi only exists for those of us who can think about it, and those thoughts are located in our brains. We can create computer programs to compute approximations to Pi. It's reasonable to say that those programs also think about Pi, and, again, those thoughts are located at particular times and places at which those programs are running.

So the (abstract) number Pi has no location, but any thoughts about it have specific locations in the brains or computational devices that are having those thoughts.