What is this grass? - Crus galli

This grass is growing in my garden. It seems to be very happy with no rain and barely any water left in the soil. Where there is no competition, it grows quite small and flat, sometimes as small as 4 inches across before starting to flower. But where there are other weeds, it grows upright and is at least 4.5 feet high - almost as fast growing as amaranth weed.

As the plant grows, it develops a beautiful red tinge on it's leaves, and the seeds are turning red-ish as they mature. The segments of the stem are marked by a red line.

It seems to be an annual, and I first noticed it about a couple of weeks before our last frost date - just about the time the rains stopped.

The soil is silty/sand, in a small valley that slightly floods every winter.

The grass stocks are sort-of flat-ish... if that makes any sense at all.

Does this grass have a domesticated relative (ie, edible grain)?

Given how well this grass grows in our dry summer and how easily it competes with weeds, I was wondering if it would make a good starting point to breed some grain that grows happily Fukuoka style.

I'm wondering if this might be barnyardgrass.

Echinochloa crus-galli
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According to the second link, it is edible, but the seeds look tiny. I wonder if it's worth investigating breeding a more domesticated version of this grain? Do you think it would cross with millet?