Great plant you have there!

I have never kept one myself but I do know they are extremely tough plants. They grow on the sides of mountains in grit and are very hardy. I can't see any reason why you couldn't dig it up and pot it.

Make sure the potting mixture has very good drainage and it needs a good amount of water during the growing season.

You should think twice. Why? Because in the ground its thriving on no care. Once you dig it up? Its a baby forever,needing to be watered in summer every other day or so,trimmed,and that routine must be done or it will die. In ground? I would trim it way up,to expose that caudex..and then set it off with a nice gravel mulch of choice and complimentary rocks.
I think leaving it will be the wise choice in the long run. You can always Bonsai a nursery plant..and then you will REALLY appreciate the in ground's no care.

I agree with Stan, it's best growing in the ground for the plant - while not meeting your aesthetics (and I've been there too) the plant clearly will likely like it more PIG'd (planted / placed / put in ground) than it will PIP'd.(placed / planted / put in pot). They're naturally liking it more in the earth and they grow better overall in the ground, not the least of which is more disease / insect resistant.

I toss this thought out there for the far more knowledgeable to evaluate as perhaps a possible compromise between aesthetics and ease of care ...

What about it the OP continues growing it in the ground but raises it up to expose a bit more of the caudex?

As I have zero experience in this area, I'll be interested to hear what others have to say.

Wont work Paul. In ground plants have roots that can go out for yards. They become one with the soil. At best, trim up,wash a way a inch of so of soil around the base.
He can always Bonsai a container plant. And when that gets old,he will be glad he left Methuselah alone!