Beautiful! I was also going to suggest starting some cuttings, then deal with the mama plant when those are growing well. Removing a lot of the leaning lower branches would yield a lot of material to make new starts, restore a more upright appearance for the mama plant, and make the mama plant easier to handle.
If you are looking for a new pot, I would look for another unglazed clay pot, which ameliorates most of the concern about root rot/overwatering because it breathes and allows roots to access much more oxygen much more easily.
Many plants of desert origin really struggle in "good soil," so gauge the necessity of providing that by the plants' health, not the appearance of the soil. From what I can see with the background glare in the pics, your plant does not look unhealthy.
