Hi Kevin,
I apologize for the delay in getting back to you. Thank you for uploading the images. This is an interpolation ringing problem with the default Lanczos interpolation used by StarAlignment. The bloomings are jump discontinuities that tend to generate strong ringing artifacts with any interpolation using an interpolation kernel with high-pass components. The ringing clamping algorithm prevents dark ringing, but at the cost of generating bright artifacts around the bloomings. This is a difficult problem but fortunately we have a good solution: drizzle.
In StarAlignment, use bicubic spline interpolation. This will still generate some ringing artifacts, but much smaller than Lanczos. Another good option in this particular case (not on a general basis!) is bilinear interpolation, which cannot generate ringing because it does not apply any high-pass filtering. The price to pay is much more aliasing, which reduces resolution. But this is not a practical problem if you use drizzle at the end of the process, since the registered images won't be used to generate the final integrated image.
Remember to enable generation of drizzle files in StarAlignment. Then use ImageIntegration to update the same drizzle files with pixel rejection and statistical data. Finally, use DrizzleIntegration to generate your final integrated image. Set drizzle scale = 1 if you want to preserve the original image scale and get better SNR, or try with drizzle scale = 2 if you prefer to work with a better modeled PSF at the cost or more noise. You have a good bunch of images, so you can try several options.
The *huge* benefit of drizzle integration is the total absence of pixel interpolation. This means absolutely no ringing and no aliasing artifacts, which is really great. In my opinion, DrizzleIntegration is the best option, in general, to achieve optimal results with any type of raw data in PixInsight. If using raw CFA data, enable CFA drizzle. If the images are undersampled and the amount of frames is reasonable, use drizzle x2. Otherwise, or if preserving the original scale is preferred, use drizzle x1.