I have run into a similar challenge. I have a calculated Dimension that I created just to limit the number of years that are displayed in the filter and chart and want to ignore the values in my Set Analysis expression when they are selected.
It doesn't work.
It would be nice if the new calculated dimension had a new field name that you could use.
I don't think that you can get this to work as you are trying it. The only thing that I can think of is to remove that expression from the Dimension if possible and calculate it somewhere else. Then just reference that as the Dimension. Then you are just using a single field or variable as the Dimension and it should work as expected.