Thank you all!
I till and amend my raised beds until the soil is half-decent, so re-seeders can have a hard time. But I weed carefully around Dianthus and Salvia ... but the Salvia bed was SO overwhelmed by weeds that there were no Salvia left to worry about.
It take me a few years of amending and growing in my soil to bring it up to "half-decent". Growing only annuals and vegetables works for me, so I can weed it 100% twice per year, and keep turning bark and other organic matter under to break up the clay that returns as compost is digested.
I have yet to fully control weeds in beds with perennials or re-seeders. Once bulbs die back, I can use a scuffle hope on the surface weeds. I have some yellow California Poppies that come back thinly, and they get more hand-weeding than most other beds. I want to get some Mikado Poppies established the same way.
The Alyssum win because they grow where nothing else will grow, and they out-compete the weeds. They're like a lovely, sweet-smelling cover crop. But they don't make very good cut-flowers, they sprawl too much.