Then I found the following comment by Carolyn Priest-Dorman in a web article she wrote about Viking Age stitching:
The running stitch forms the basis for almost all the seams in the textiles that this work discusses. However, it was not the only stitch used in the period to construct joins between fabrics. At Jorvík, a common way to join two pieces of silk or wool fabric was the overcast stitch. It could join raw edges on wool, folded-under edges on wool or silk, or rolled edges on silk (Walton 1989, pp. 407-8). The seams on the tenth- and eleventh-century Hiberno-Norse caps from Dublin provide evidence not only for running stitch but also for whip-stitching. One interesting seam variant from that site involved turning the two edges of a seam toward the inside of the cap and whip-stitching the seam from the outside of the cap (Heckett 1987, p. 167).(emphasis mine)
Many different methods existed for finishing a seam neatly. At Jorvík, sometimes the folded-under edges of a plain seam were individually sewn to the inside of the underlying textile. Flat-felling, or "run-and-fell," was also common at Jorvík, on linen: the initial seam was sewn in running stitch, and the folded edge was then sewn down in overcast stitch. Variants of flat-felling and plain seams, both of which involved an initial seam in overcast stitch instead of running stitch, were the most common seam finishings at Hedeby.
So close variants of what Laura Mellin referred to as the "Elizabethan seam" also show up in the Viking world during the 10th and 11th centuries. That's almost like...documentation for use of that seam on my 10th century himation.