CG, The alcohol is to (1) kill any germs that might be lurking from the rotten part and (2) moisten the area to have rooting powder put on it, so that the rooting powder adheres better. Knowing (or not knowing) Spanish has nothing to do with the Spanish Inquisition, but that's a tale for anther day.

You need to cut off all that rot ASAP, before it spreads. Cut up until you see completely green growth, no rot. You will have to let the cut dry for a week or so, before trying to root it. No water at all until you have roots. Christopher

Rachel, it's very hard for me to make an assessment when I am not physically there to examine your plant. I don't quite understand what you mean by soft but not overly. I see that your last picture you had lost a couple of stems, so perhaps if its really rot setting in the base, you need to catch where is the rot happening at. If it's right under all the stems towards the roots, you are better of cutting off as much rot/brown portion as possible until you see healthy green stems, and try to root the cutting as best as you can. At this point, you can try to snap 1 or 2 healthy cuttings at the tip end towards the base. Always let the cuttings dry up and callous before their to root them in new soil. And also make sure when you snap them apart, the stem must be close as to the root base as possible, if you can snap some roots with the stem even better.

I would say the same procedure. Watch for glochids on 1st plant (they are PITA to get out). Cut 2nd plant closer to green part, take off all dead leaves so you have a short stem. They usually root and there seems to be some life in them...