I do the rod repairs for a local tackle shop and removing the remains of ring whipping epoxy is a regular task.
There are no solvents, that I know of, for cured epoxy.
Most of the finish will come off with the thread but, as you may have discovered, it's the overlaps that cause a problem.
First line of attack is to try to flick off as much as possible with the back of your thumbnail and if this doesn't shift it all then use heat to soften it.
The best method that I have found is to use the gentle heat of a hair drier. If you can prop this so that the air flow is over the area of the blank you wish to work on then you can use one hand to rotate the blank and the thumbnail of the other hand or a plastic scraper (old credit card or similar) to remove the epoxy.
Always work inward from both ends of where the whipping was as this way if any thin deposits (smears) are left you can cover these with the new whippings (provided you are replacing a snake ring with another snake and not a single foot ring)
The resin that holds the carbon mat together is cured at quite high temperatures when the blank is formed, much hotter than your hands will withstand, so it is unlikely that you will damage the blank using this method.
Scraping with a sharp steel blade is not recommended as it is very easy to slice into the fibres of the blank if the blade is held at a normal acute angle. However, if you have to remove large areas of the actual blank finish (not thread finish) the safest way to do this is with a very sharp steel blade held at 90* to the surface but this requires a soft touch (and practise).
Dave.