The key is intentionally trying to go as fine as I can.
The section I did today - on the original - is the lightest secion on the model. So I intentionally focused on going with a light touch, with a finer spritz. The result - at least to my eye - is the closest I've come yet to the original.
I wish I could just redo what I've done already. But I can finesse the other areas. I will just spend some time each work session hand painting out the largest dots, the adding back in much finer black dots. Over time, this should slowly increase the degree of granularity, making it appear more fine.