Generating point on surface

Hi all,

Im quite new to rhino but I have this rather “simple” issue where I want to project points onto a surface. I would like to have the points in a hexagonal grid (potentially I want to adjust between different pattern of dots). Is this something that is possible?

As of now, I have used the Paneling tools → Create paneling grid → Surface domain length (gap between points to 0.3 but should be 0.003..).

Then I have used the Paneling from Grid → Panel 2D Grid to make pattern from a curves.
I have used this curve to find all the intersection points which gives a point grid on a surface. But I want to make the point grid even more dense. Does anyone know how I can do this?

File is here: 3315_Afriver_066_bg_QC.3dm (7.8 MB)
Picture of the current point grid is here:

Looking forward to hear back from you all!