how can I stop euphorbia / cushion spurge

I planted 9 small cuttings two years ago and now this plant is taking over the garden, even though I put down a 6 inch root barrier. I was told this was enough, as the roots are very shallow with spurge. Guess my source was wrong.

Does anyone know how deep a root barrier you need for spurge?

Finally, I thought spurge only spread by rhizomes but have just learned they also self-sow. Will cut the flowers before they set seed this year...but meanwhile I want a better root barrier.

Thanks in advance,
DR

If you've been letting them go to seed, are you sure the ones that have "escaped" the root barrier weren't ones that came from seed? I honestly don't know how deep of a barrier you need with these, just wanting to make sure you actually need to go to all the trouble of putting in a new barrier, maybe all the escapees were seedlings.