i would probally root the top heavy stems and throw away the base

Cut the three blue-green pieces off at their base / where it turns brighter green. Throw away the rest, as suggested. Set those three pieces aside for several days, then pot up in porous soil (set them slightly in the soil - you might need rocks / pots to hold up the cuttings) - just a little contact on/in the soil is needed. Put in a warm, sunny place, and begin misting daily / every other day / every third day. You should start to see growth within a month or two. When it's warmer outside, put the pots on sun-warmed soil, as bottom heat promotes rooting (if you have a heat pad you can also do this now). The base of the current plant got that way because of too little sun / other bad cultural practice(s).

Couldn't the base also be saved at the point where it is still wide? Some pups may emerge from it.

Id cut the new growth, let them callous and replant. Id also cut about 4 inches from the dirt line and let the cactus put out some new growth there. Looks like for a long time it had some terrible lighting and now that it has good lighting its putting on some good growth. I wouldnt toss the 'stump' see what it will do:)

Update: I followed everyone's instructions, and cut off the dark green sections of the cactus, let them callous over, and re-potted them.

I also saved the bottom part, to see what would happen, as suggested.

The photo is of the bottom part with it's new growth, and one of the sections I cut off, plus a pup.

I also have another pot with the other two sections I cut off, which have now rooted.

Pretty forgiving cactus, whatever it is!

Thanks for your help, all! :-)

Lee

Awesome! I love follow-up posts.

They look like they're much happier this way, and will really thrive for you on nice, sturdy bases (and I get such a kick out of that little flamingo!).