Hi Colin,
Unfortunately, I'm not sure if there are any sources of sea beet in the US that make seed available to individual growers. If you have any connections to friends or colleagues along the coastline from Denmark down into the Mediterranean Sea, the estuaries therein are good sources of
native sea beet growing wild. Otherwise, you may want to make a trip to California to see if any of the invasive populations are there to be found:
https://www.calflora.org/app/taxon?crn=11374
Good luck!
PS.... If you have contacts with others living along coastal southern California and they can ID the plant, they may be able to find some seed from last year's stalks. I can't recall off the top of my head, but sea beet may be 'segregating' for annualism......some will want to flower the same year that you plant them, but others will not flower the first year and you would harvest the
root, cellar it overwinter, and replant the root for flowering and seed set in the next year.