Regularized variable element removal

Dear helpful people,

I have a grid of circles that are organized in a running bond pattern. While staying within this grid pattern, I am trying to selectively (but not randomly) remove circles  to create a nice linear gradient(as shown in the snapshot).

I've tried various combinations of CullNth, PathMapper, functions, introducing a variable element through distance along the Y-axis but all efforts ended up looking very striped.

Since the top section has to maintain the original opening distribution, in the Baseline file I have divided the rows in the top area into two sections: the section that will stay unchanged and the section that will have the gradient. 

I have been trying to reverse engineer the top gradient for several days now. I would like to be able to generate it parametrically and vary how quickly the fade happens, the size of the panel, etc. Currently, I am choosing which circles to keep, remove, and the row spacing on a 8,5,3,2,1,1 variant (roughly). I would like to be able to create some version of it parametrically that would allow me to produce a similarly smooth gradient. However, if anyone has an idea of how to make a smooth linear gradient using any sort of pattern I would be grateful for suggestions.

I have a feeling that there is some way to do this and I just don't know the right pieces to put together. Any suggestions would be much appreciated!