Another possibility is that the green leggy specimens you found may be new ajuga plants that have "reverted". Ajuga "Burgundy Glow" is a cultivar, and was bred to be that burgundy color. But it doesn’t always come true from seed. This means that if the Burgundy Glow makes seeds, and the seeds fall on the ground and grow into new ajuga plants, they might "revert" and not look like the orginal burgundy-colored ajuga plant that you liked. The new plants that grow by themselves may be green or even bronze-colored.

Some people deal with this problem by removing any green-colored ajugas that may appear in their Burgundy Glow ajuga patch. I've heard of people even removing the ajuga flowers once the flowers have faded, in order to keep the Burgundy Glow from making new seeds that could grow into green ajugas instead of burgundy ones.

About the growth rate: Ajuga "Burgundy Glow" is good for covering small areas, but is not great for covering large areas, because it grows more slowly than other kinds of ajugas. Some ajugas that are more invasive and will cover large areas faster include the plain Ajuga reptans (which has green leaves), and Ajuga "Bronze Beauty".

P.S. Ajugas also spread by underground roots known as runners, so the piece with the plant root at the end that you pulled up may be one of these underground runner roots. New ajuga plant shoots eventually will form from these runner roots.

The Ajuga Bronze Beauty has leaves that are pretty much green...sort of a shiny green-ish brown, and it has blue flowers. Bronze Beauty is definitely more invasive than the Burgundy Glow, but it probably won't choke out your hydrangea, since shrubs like hydrangea are pretty tough and have deeper roots than ajuga.

The only thing that may be a problem is that the Bronze Beauty and other more invasive ajugas can spread into your lawn, and I've heard they are very hard to get rid of once they get loose in a lawn area. Bronze Beauty may also crowd out your Burgundy Glow somewhat.

Also, with an aggressive ajuga like the Bronze Beauty, it would be hard in the future to plant any other types of perennial plants in the same area, since it may choke them out too.

An alternative option you may want to try is filling in any bare areas in your Burgundy Glow patch with one of the burgundy-leaved Heucheras/Coral Bells. Heuchera doesn't spread at all like a ground cover, but they come in some really great burgundy colors nowadays, and the leaves will stay burgundy and not turn green.

You could try one of these varieties of Heuchera:
"Amethyst Mist"
"Plum Pudding"
"Palace Purple"
"Sparkling Burgundy"
"Plum Royale"
"Midnight Rose"
"Berry Smoothie"
"Smoky Rose"
"Mahogany"

These all have burgundy, pinkish, purple, or red-colored leaves. You could even combine a few varieties in the same area. I've planted Heuchera a lot this year in our shady spots and have had good luck with it so far.