Counting values across multiple rows based on primary column

I managed to track down part of an answer but it didn't solve the entire issue. I can expand on the sample table I included but that's the only example I can give. My half-solution is calculating a union table that combines all the primary-secondary-and so on columns into one, then counts the rows that match the distinct values drawn from those columns.

So while my first table looks like

My expected output looks like

I'm getting the second table with the calc - union approach, but the lingering issue is that my original data table also has a date field and once I create the visual based on the calculated union table, it doesn't filter based on the date, which is only affecting the original table. 

So I'm hoping for a way to calculate the same output values in a way that maintains the relationship between the primary table and the calculated union table so that filters applied to the primary with also affect visuals made from the calculated. Or some other way to simulate the effect.

I tried creating a bar chart and dragging all the response choices (primary, secondary, .... all the way to 30) into both the axis and values fields and then changing the colors to all be the same to it looks like one bar and not 30 rainbow pieces, but that's not ideal.

Sorry if this isn't super clear, I'm stumbling my way through this project