I suggest you cut off the last leaf, leave the rest to dry the cut (I usually do it for 1-2 days) and put it in a glass with water as you wrote. Place the plant in a very warm place, change the water every day, the roots should appear quickly. Now it is warm and a very good time for rooting. And good luck :)

I also have 'Eve' and I noticed that compared to 'Whitney' it grows much slower and is weaker. I have both for over 3 years and at that time, 'Whitney' grew very well, a lot of pups, and split it into 2 pots, and 'Eve' released only one and is still very small.

Here is my 'Eve'

I had the same thing happen to one of my sans. I removed it, let the end dry and put it in it's own pot with fresh soil to root. It's in a shady area on my porch and after a couple of weeks feels like it has already rooted.

to add to Stush's comments, "only moist"- use a spray bottle to just dampen not soak the perlite.

Rooting in perlite does not work for me, I can't do it :)

At the end leaves are going to the rubbish.

After cutting the leaves, I always put them in water

and after a few weeks they look like this

Thanks for all the suggestions. I anticipate I will overwater the perilite, although I've never tried it before. I have successfully kept some plants in a glass of water, while others get moldy. I don't know how to predict what will root and what will mold...

If you're using sand or perlite, dip the bottom of the leaf into a bit of rooting powder. It helps greatly with root development.

Some of the rooting power has a anti-fungle so it helps. If using the water method, keep only enough water to cover the bottom of the leaf and change the water at least weekly. Fresh water had more O-2 which is what the young roots need. A touch of Rootone mixed in the water helps too. Once a tiny bit of rot occurs, it's toast. That's why I use the grit method.

If rooting in water, do you put in more rooting pwd every time you change the water? I just bought some, but I have a leaf I've been trying to root in water for about a month now without rooting pwd. Can I add some now?

You could always add rooting power when you want. Should only use a pinch. Most effective when first using. It might be a waist after wards but not harmful.

UPDATE: I left this plant as it was and put it outside for the summer months. I brought it back into the house in August. Even now in January, it looks the same, not dead, but no new leaves. The disease had killed any new leaves in the center of the rosette, so I suppose the only hope would be new rhizomes.