I did the alignment of the 20 frames manually in Gimp, but had to convert the images from 16 bits depth to 8 bits in the process (Gimp 2.8 apparently only supports 8 bit depth). I then fed them into PI, see screenshot:
- top left: ImageIntegration with average, clipping pixels with value 0. Settings are as shown on the right of the screenshot. Differences are clearly visible.
- bottom left: same, integrating with maximum values. Differences are even more visible than with the first attempt

- top center: result with GradientMergeMosaic. Default settings as shown on the bottom center, only setting Shrink radius to 10 to get rid of some pixels at the border of each image. Seamless result

I did not do any further processing. I suppose if you can preserve the 16 bits, you could make a fairly spectacular image showing even the flares at the sun's border. Unfortunately, neither Gimp nor PI (see
http://pixinsight.com/forum/index.php?topic=4356.0) has a suitable tool for doing the alignment while preserving the bit depth.
Georg