I've been experimenting with sauerkraut this year too. The last batch was my absolute favorite, fermented in a sealed jar with an airlock. No worries about mold or air contact. Chopped up 10 lbs of cabbage (some red) and let it go a month controlled to 68F. It was summer time and didn't want to risk it getting too hot. Turned out great. The first batch I ever did I pitched a starter made from the sauerkraut juice (exclusively) into a Gose wort and it turned out surprisingly well. It was rough at first but came around after ~4 months.
Freshly chopped:
After a week or so. Should have installed a blow-off tube!
Culture pitched into the Gose wort:
Fermenting: