I wonder if the spraying was done in sunlight. Alcohol and heat will burn and scar a plant.

Burning and scarring will not cause a plant to rot from the inside out, though. Did they perhaps get damaged around the base during repotting, allowing rot to set in?

Sounds like root mealies. It would be very difficult to get them all just by changing soil and spring with alcohol. You're better off using a systemic like Bayer Tree & Shrub (imidacloprid) that's mixed in when you water so it gets taken up by all the plant parts and makes the whole plant toxic to the pests.

That's why I asked if there was any damage to the bases. rot can affect plant parts other than roots...

I imagine it would work. Can't hurt to try it.

I had root mealies on one of my plants; discovered them as I was repotting... I thought I'd gotten all of them off when I washed the soil off the roots but was wrong. As I'd already have an infestation some month back, I decided to use insecticide straight away instead because the alcohol and water solution never really helped... So far, no more signs of mealies.

I don't know if the insecticide would do any good, now that your plants have started rotting, or whether they are salvageable... perhaps you good try propagating? I don't know how that works exactly with cacti...

I've only discovered root mealies on two plants and both times they were visible... no moldy, white dust, though...

...could it actually be just that? Mold?

I think the dying center might be a red herring. The tough outer skin of many cacti will hold up a long time after the plant has died, giving the illusion that the plant is still alive even as the xylem and phloem are rotting away inside the shell. I used to find completely dried out cacti in AZ all the time, just a hollow shell that often looked alive, or still stood even though the color had gone out of them. What caused their deaths, I don't know. They were wild cacti, or at least outdoor cacti, and none were mine.

The threads of web you mention can be left by some species of spider mites. Not all leave webbing, but some do. Some spider mites can be invisible to the naked eye. I had a couple of plants get them and the first was infected for about 5 months before I finally figured out what was wrong with it. I would think that spider mite damage would appear on the surface long before a cactus died from it though.

Are these indoor or outdoor cacti? How long have you had them? How long have you been growing cacti. Can you upload some photos of the root systems of affected plants, the soil of affected plants, etc? Is the outer shell that's left dry, or is there still some moisture in it?