I wrote some software back in 2006 to align around 30 total eclipse pics, because I couldn't find anything "off the shelf".
15 years of tweaks later and I'm ready to print.
The centroid of an annular eclipse will shift so it'll be hard for any software that doesn't also do edge detection.
ED is hard when you get to fluffy solar "edges" 3000x2000 pixels or suchlike. The matrices become large and slow.
So my algo reduced my 3000x2000 images to 300x200 to make it faster first time round.
I had a dual core Pentium back then - oh yeah. A doubled stacked CPU.
To cut a long story short - nothing beats the human eye for KISS principles.
Bring image #1 into Photoshop or suchlike.
Bring image #2 into Photoshop or suchlike. Set the layer merge to "difference"
Use keyboard to move one image relative to the other.
When the two are aligned the difference will be nigh on blackness.
Rinse and repeat for the other 99 images.
I promise you that's quicker than faffing about with software for 15 years
As for making all frames of an eclipse "equalized", I would say it is that loss of equilibrium which makes an eclipse so profoundly unsettling (to the neophyte). In Turkey 2006 I went from hot and happy to shivering and not able to use my camera properly because I had no idea "when you turn the sun off" it gets so cold so quickly.
It's a fine balance - the art or the science. Humans are great at both.
Although me personally - neither