Take cuttings of firm new growth. apply 0.1% IBA (rooting hormone) stick in well drained soil & mist takes 15-40 days to root

Amelia I am risking here to repeat myself...but: -if the soil is too moist for too long, it is either too water retaining or there is no drainage holes in the container or perhaps both -it could be cooler in your office because of AC (I am guessing here) and it takes even longer for the water retaining soil to dry out -top layer of soil - according to you - where if it remains bone dry for a period of time the top layer becomes tough - this is very likely because there is too much peat (peat dries on top, gets crusty, but often is very wet below). -shallow container for starting plants from leaves is fine, watering in any container - shallow or deep - is no problem if one uses well draining potting mix. Actually, they don't even need soil - here are some extra leaves from similar (perhaps same?) plant that are just sitting there - no spritzing (this is relatively recent): and as I previously mentioned that I leave many in the original pot and don't do anything 'special', here you can see many that have grown from leaves: This plant has longer leaves than Sedum morganianum (burro's tail). It was ID-ed as Sedeveria 'Harry Butterfield'. Leaves on your plant seem to be just a touch shorter but longer than burro's tail), I would think it is Sedum morganianum 'Harry Butterfield' - I have seen it described as such. I could be wrong...? -I water succulents more often in the warmer weather. Leaving them to signal every time that they are thirsty by shrivelling is perhaps adding too much stress. In gravely mix I use, danger of overwatering is very, very small. I would like to add, that any response here should be read and see if there is anything useful in it for person asking. I understand that written word is harder to 'feel', but just about all responses on this forum are offered as an answer to a questions asked, sometimes very direct, but that doesn't mean person offering advice is being rude. Very often ppl ask a question and don't like the answer. That doesn't mean poster is rude. And sometimes it could be wrong answer. Nothing wrong with that. Everyone here is a plant lover, many ppl are new members and many are 'long-timers'. We just share tips and experiences, offer advice, ask questions, try to correct incorrect answers - that could be bit touchy too - I don't believe anyone here has different reasons. JMHO. Celeste IMO, the soil you are showing in your photo is too wet. Not only because it is dark (that is usually a good indication), but perlite is becoming discolored too, and that happens fast with too much water. I know you didn't ask, I am just pointing out what I see in the photo.

My sympathies, I've had an awful time with these. Mine do exactly what yours show in the photo. I do have one or two containers now that are getting nice size on them, after I moved them into mostly shade on a friends advice. I use rooting powder to root them in coarse sand, it still takes about 3 months or more. I have 2-3 types and have all the same issues with each. Sorry not much help. My suspicion is they like a warmer climate and plenty of water. I think it's hard fo me to give the right water because it's so cool here overall, which makes it easy to over water. Just a theory. But the successful rootings I had recently in coarse sand have been with no water, just left in the sand dry until the roots are really really full. That's because when I transplanted before with scant roots they'd just decline and die.

This cactus definitely likes more water than other cactus, but still let them go dry before watering again because they can rot. These guys hang off the cliffs of Bolivia in the jungle. So their roots are constantly being washed with water, but their roots are never ever sitting in a wet mix. A good gritty mix would work nicely. I keep mine hanging in a mini apple tree, but obviously you can't do that in your zone. They like bright filtered light. Not direct sun. Definitely do not like the cold. So far Monkey Tail has been one of the easiest and fastest growing cactus I have grown:).