How do I add a sour mash into a BS recipe?

My wife and I recently brewed a Gose using a sour mash. We added three gallons of sour mash to the first runnings of a normal mash for the boil. I would like to add this to my recipe in BS just to keep things accurate and get better projections. Any idea how to go about it?

Make the sour mash a separate recipe with no fermentation profile. Add the sour runnings to the main recipe as a sugar addition equal to the sugar weight of the solution plus water volume.

Makes sense thanks for the help.