What you could do to encourage more of the white plants is to relocate a couple to a space of their own to spread. You may still get a few purple plants that pop up, but you can cull those as they do. I wouldn’t take all of the white plants from your original bed until you know that the first few you relocated are surviving and thriving. Good luck!
Plants are often a wonderful reminder of and tribute to the loved ones we’ve lost. Nice that you’ve got a connection to this particular plant. Best of luck!