I always read up heavily when a plant catches my attention. 
The bleach solution itself was Mr. Winterton’s idea.
My Society Garlic is actually sending up a bloom right now, before re-growing the trimmed leaves. I gotta take a pic when it opens fully.
I found another species to try that’s available through eBay, so I’ll be getting it soon. Allium canadense. I had ignored it before because the name implied (to me) a necessity for cold, but as it turns out, it grows well as far south as Florida, and even Cuba, so it’s fair game! I’m slightly concerned over a source claiming that chronic consumption reduces iodine intake, but I guess it’s as easy as eating in moderation and seasonally (instead of constantly). According to Green Deane, it has strongly garlic-flavored bulbets and mildly onion-flavored bulbs. Video here:
