How to create a very accurate STL file as well as the slices for a 3D printer?
Your objective has a serious constraint regarding the pixel resolution. Within that limitation, the software (slicer) you are using will generate "best guess" images, particularly dependent on floating point math. There may be a single combination of circular shapes (radius) and spacing for these shapes that provides your objective, but that's likely not a practical exercise.

You have not indicated if you've tried other slicers, which would be the primary direction. A list of choices can be found here:

Free Slicing Program List

Another option that you can consider, not included in this list, is to use OpenSCAD, import the STL file, then use the projection() command to manually slice and export the image file. I use the term "manually" but the program can be coded to perform this task automatically, and there is a command line feature to OpenSCAD that may be useful.

Note also that the output of these slicers and/or OpenSCAD may exceed the resolution you desire. Manipulation of the image with a graphics editor could result in the same floating point disarray as you perform the changes.