3 hours ago
Still not sure what is required 
Instead of fuzzy select maybe use color select to obtain a white BG (leave alpha off for the moment). Color select with draw mask enabled - click and drag to define a selection then Edit -> Cut then Select -> None.
Now apply color-to-alpha and you might have more success with the white BG.
Sometimes the eraser tool in anti-erase mode can restore parts of the image.
For tweaking transparency. The curves tool using the Alpha channel.
Some of that might / might not be useful. I can just get it into a 60 second animation https://i.imgur.com/0WrmryZ.mp4
Another possibility is the gmic_gimp_qt plugin which has an interactive-extract filter, but that is different story.
Instead of fuzzy select maybe use color select to obtain a white BG (leave alpha off for the moment). Color select with draw mask enabled - click and drag to define a selection then Edit -> Cut then Select -> None.Now apply color-to-alpha and you might have more success with the white BG.
Sometimes the eraser tool in anti-erase mode can restore parts of the image.
For tweaking transparency. The curves tool using the Alpha channel.
Some of that might / might not be useful. I can just get it into a 60 second animation https://i.imgur.com/0WrmryZ.mp4
Another possibility is the gmic_gimp_qt plugin which has an interactive-extract filter, but that is different story.