If it were mine, I would cut each stem, leaving about 2 inches below each leaf bunch. Pop off solitary leaves. You can let each piece of Sedum pachyphyllum ;) heal for a few days before re-planting in a gritty mix.
The rooted stems will also continue to grow new heads after being cut.

I've found many a Crassulaceae (yours appears to be a Graptosedum or something so) behind / below a potting bench / shelf, rooted into the chin dribblings, as it were. You can see some Graptopetalum superbum leaves which have rooted into plants.

You can plunk him into C&S soil as is, loosen completely the soil around the root ball, or somewhere in between - it's up to your level of desired work. That's what's great about them, or should I say, another thing great about them.

Personally, I'd take the path of just a little resistance and shave the corners into half of what they are now and put it into well-draining soil. Water in a few days after repotting and away you should go.

Thanks for the ID too. ;)