Peter,
The answers, I think, depend on what you're describing as a time lapse – is it a video sequence that speeds up the passage of time to show the eclipse at an accelerated rate (this appears to be what you're doing), or is it a series of still images you're assembling into one or more 360° panoramas to illustrate the sequence of the eclipse?
I did both back in 2017 for the "Great American Solar Eclipse" that we experienced here in the U.S.
I found the easiest way to do the video sequence was to do it in Photoshop, by importing each image as a layer onto a video timeline, and then manually aligning them with each other. The aligning can be best done, I found, by setting the subsequent image(s) as slightly transparent (70%-80% transparency), and aligning via sunspots and edges of each one. Align each image in the sequence with the first one, rather than with the most recent one you aligned, in order to avoid compounding errors. Then, reset transparency of every frame to 100% and output as a video from the video timeline, with whatever time amount you want each frame displayed and an appropriate transition between each. Tedious, yes... but quite doable
It would be far less so if your equatorial mount had been aligned properly and every image was already aligned in camera. Most video producers know that "fixing it in post" traditionally takes 10 times as long and costs 10 times as much as doing it right while you're shooting. Unfortunately, we don't always have that ability (or luxury, it sometimes seems). :-)
The 360° panorama sequence was far more complicated, both in shooting and post production. Mine was planned as an all-day sequence from dawn to dusk, with sun images shot every five minutes to allow for good spacing between them on the final panoramas. I also shot full 360° panorama sequences at different times of the day in order to show the progression of the sun across the sky and to more accurately be able to show the environmental lighting as the day (and eclipse sequence) progressed.
Post production on this one also required compositing in Photoshop to ensure that the time lapse sun images lined up properly, followed by stitching of the composites in PTGui. Most of the source images were shot with a solar filter *only* covering the area of the sky where the sun was positioned in the frame. This allowed accurate alignment of the sun between frames using non-sun portions of the recorded images for alignment reference.
It all took a tremendous amount of planning, testing, and post-production time – but the results were worthwhile. :-)
Scott
Scott Highton
Author, Virtual Reality Photography
Author, Virtual Yosemite