A script is probably the best way for doing this entirely within SolidWorks, and perhaps someone has made one.
SolidWorks can fit a spline to a bunch of line segments, but I imagine you need a true circle.
If you have access to other CAD software there may be some functions (like circle or arc fitting) that would make this an easy task. I'm sure there is a script for AutoCAD or IntelliCAD to do this
If you are pressed for time, take a look at BackToCAD, they have an app called Print2CAD that does circle and arc fitting. I have not used it myself for this function, although there is a trial available to test it. Its reasonably priced, and might be useful to you for other things as well.
Are the "several hundred holes" in a pattern, or groups of patterns?
Unfortunately no, they are random in location.
I was thinking a script as well, I just don't have any experience with that within SolidWorks so not sure where to even begin/look.
Will look into the BackToCAD...
Is it that SW Document Options is set to coarse display of arcs as polygons? I can't remember the name of the control.
Are you thinking of Tools/Options/Document Properties/Image Quality? I'm not sure how the "Shaded and draft quality HLR/HLV resolution" and "Wireframe and high quality HLR/HLV resolution" sliders would affect DXF files, but I assume that setting them low would cause circles to look more obviously polygonal.