They were cobalt flats, not rounds. Going through the string forum at the time, I did see where others had the same complaint - that despite callouses, fingers became sore. The best theory is that tuning to pitch ever so slighty opens the ribbon creating a cheese grater effect.
The cobalts were replaced with chromes and the issue stopped immediately. So, it was clearly the strings.
It could be a QC issue at EB. They have had other issues with the cobalt flats in the past (along with weird installation instructions in an attempt to correct the problem), so it wouldn't surprise me if it were one (or more) bad batches. However, there are many strings available, so I have no need to go back to strings with which I had such a poor experience.
With poor experiences using cobalts and being very underwhelmed with the sound of slinkies, I think I am done with all strings coming from EB. I have favourites from D'Addario and DR. I have also had positive experiences with Rotos and still have an interest in trying SITs so it isn't as if I were out of options.
Perhaps one day I will try flats again (perhaps Roto 77s) but trying tapes is a higher priority.