Thanks KyL and pokoy.
It makes sense that the black pixels were exceedingly bright. The eyedropper in post measured them far above the 1-255 range (far above 100,000 actually; they were likely over 10,000,000). I didn't realize exr's had NaNs limits.
Neither the Cubic B-spline and the Catmull filter worked in this particular case to eliminate the black spot, but increasing the sun angular diameter even to 0.65 was enough.
Saving the problematic exr as an hdr, then painting over the hdr worked too. The issue to be aware of with this workaround is the quality of your painting. Even after I had painted over the black spot, once I reduced the exposures 6-8 stops, the sun had a gray halo in the center where my painting was not perfect. Getting the right intensity spot on is up to the user's talent.
Thanks,
Matt