I would not cut them off. These are not offsets as aloes produce. These are branches. In my opinion these plants look much better, if you leave their branches where they are. They won't suffocate your plant. A tree does not die because it's forming branches. If you want to propagate your plant you can use these branches of course, but I would wait until they have grown bigger.

Hi Bethan. Nice plants. I love the pink edges on the leaves. I'm not one of the more experienced growers here, but I've been helped by many and follow the stories of plants in trouble. It's much easir to diagnose a plant's problem if we know the climate/area you're in. And you'll be asked questions and told a few tips on things from the photos. Good photos by the way. As I indicated I'm no expert, but maybe the problem could be stress from the move? Generally it's advised not to have plants double potted as it creates a lot of moisture sitting around the bottom of the roots, which succulents don't like. Questions - what potting mix are they in, how often do you water and how much, eg a little bit or until it flows out the bottom. Other more experienced growers should chime in. I wouldn't repot yet, if they suspect a root problem they will probably ask you to check the roots for rot and guide you from that. Hope it all works out :-) Helen

The correct name is Crassula perfoliata var. minor. They can take quite a bit of light an heat. If all they could take was 85F then mine are a few degrees dead then. They need good light to grow compact and to flower. I think mine usually flowers late summer (probably should have written that down). Checked some photos just now: It flowered for me on June 16 in 2015. The plant has reliably flowered for me every year after that but I don't think I really kept track or would have to dig up the photos. Here it is now:

That yellowish flesh may have been ok - I am sure I said somewhere that usually it is greenish color, sometimes more creamy. What you do not want is dark spots, of any size or shape. Dark like brownish or blackish. But do not worry. Let cuts callus for a while, and after plant them in dry mix. I usually do not water root-less cuttings for a while; 10 days, 2 weeks or longer. I start watering when I see some new growth - sign of roots growing. (I already said that too - sorry for repeating). Some ppl recommend spritzing with water after few days. BW, I usually trim off that longer piece of trunk from cutting too, just as I suggested where to cut from trunk. It just dries up and heals over faster. Not everybody does that, and that is OK too. What I mean is to trim off excess below the collar. Hope you understand what I mean - if not, just ask. (I just added a photo where it is quite well visible - see end of this post). You could lightly dust the cut with flowers of sulfur, or powdered cinnamon,.but not absolutely necessary. Those are fungicides. Here is photo of one thicker branch I did (I very seldom do it anymore). This shows darker flesh because it is already callused, and I used powdered cinnamon - not because there were dark spots! ETA: here is photo of thicker branch, just cut (before callusing). You could also see how far from the collar I trimmed it: