The final decision was that some sort of border was needed to stabilize the edges. The original border was not a good design and through the years had not held up well, so I decided not to recreate it. The slight visual differences between the old and new thread meant the edging needed to be small and simple -- so I started with a round of single crochets. I liked the look of this but the row "curled in" on itself and didn't look right. A second row of single crochets looked awful and I experimented with a number of single crochet, chains and picot patterns for the second row and hated them all.
The winning effect was to turn the tablecloth after the first round and slip stitch around for the second row. This produced a thin, stable and non-curling border which was exactly what I had in mind. I LOVED IT!! I worked the first row of single crochets with a size 10 hook, and this matched the gauge of the tablecloth, but the slip stitches made using that size hook were tight and pulled the edging inward so I bumped up to a size 5 hook to get them loose enough.
Unfortunately, I don't have a good way to properly block the tablecloth. So far I've managed using a stair railing and a touch-up with an iron. My Aunt remembered a very interesting device called a curtain stretcher. Lace curtains had to be washed, starched and stretched and the curtain stretcher was a wooden frame with sharp pins around the edges which held the curtains while they dried. Mom said Grandma had one and she'd take the tablecloth over there and use it for the tablecloth. They're actually available for about $10 on eBay and Craigslist. They're big and bulky and from what I've been reading, not friendly to the fingers! So considering the number of times I'd actually use it .... I'll make do.
I've picked out the pattern for the motif and written it out. It's available over in the free vintage patterns section of my website.