I'm not too surprised. I tried to save one that was much less rotten than those and I felt like I was fighting a lost cause. Even though the rot may show itself first in the lower leaves, it is in fact the heart and stem of the plant that are fatally infected. At least that's the way I see it.
Here's my strategy, right or wrong.
At the first sign of rot I take extreme measures, the affected rosette is immediately pulled and disposed. Any viable offsets are kept and replanted if not already well rooted. Presuming of course that they appear solid and healthy. If there are no viable offsets... oh well. So far I've not lost a single cultivar to rot as I've always been able to save the offsets. The saved offsets appear to carry on nicely. I'm not sure how this would work on Jovis where all the rosettes share a common stem. Or Calcareums that are tightly bunched. I'll cross that bridge when I get to it.
I also don't worry about the soil being infected. I feel like the culprit is endemic in the soil and always present. It is only when plants are weakened or has open wounds that it gets infected. It seems to me that chicks that establish themselves naturally on top of the gravel are practically immune to rot, as opposed to transplants that will have root damage, micro abrasions, and my not be set into the soil and gravel at an optimal level.