None of these two options give me quite what I want, I think.
Using the mean from before detrending generates a datasets with lots of values that are zero, or near zero, which doesn't seem desirable.
Detrending after scaling generates a dataset with a range from -160 to 200 approximately, and not 0, 200, as is usually the goal of the scaling operation.
Any other ideas? I am surprised that there is not some standard way of dealing with this.