Thanks - I never thought to soak them, despite their hard shells. Are you doing that mainly to soften the shell, or to rinse away germination inhibitors? I might try a hydrogen peroxide soak-and-rinse as an alternative to multiple soaks & rinses over several days.
Fortunately, Friday night, they were definitely sprouting on the paper towel.
Over the weekend, they emerged from the soil in a shallow bowl. Their elongation sped up on their second day up, maybe they liked the brighter light I gave them.
I got around 80% germination on paper, and 70% emergence from soilless mix.
I found some several-year-old Fall Rye seed that I bought for cover crops, so I sowed some of them in a second bowl. I hope Toby appreciates the cat grass!