So here’s what happened when I washed the new, improved, diaper wipes:
Verdict: they frayed, just as badly as the old, non-improved wipes. But the thread did end up being colorfast. (I think Marty’s hypothesis that substances other than water caused the dye to run might be correct.) And presumably, once they fray as far as the stitching, they will stop fraying. We can hope.
In the mean time, they’re no worse than the original wipes, at least!
One thing you could do to reduce fraying is trim the wipes as close as possible to the zigzag stitch. Then all you’d get are little fuzzy things.