To my way of thinking, having the amount and value of domestic goods shipped out by port, gives you that number. However, the South shipped all sorts of goods North each year for their consumption, so the port figures would reflect the GDP fairly accurately. How much was shipped by rail or wagon is another matter.
One author/economist did develop figures of regional productions that came from the census and customs records.
Name is Thomas Kettell. His work can be found on line.
It might, if you only considered such Southern ports as Charleston or Savanah.
But over 80% of "Southern" commerce went through the two biggest ports of New Orleans and Baltimore.
And those ports both had major rail and steamboat connections to Northern & Western states.
So demonstrably large percentages of "Southern exports" were, in fact, produced in Union states.
Cotton & rice were the only certain exports of the Deep South.
Combined those contributed about 50% to the cost of tariffed imports.
1860 railroads, note New Orleans & Baltimore connections to Northern & Western producers.