Any splice must be accessible so you would probably be better off with a new run of cable from the pole to the cabin.
The depth of the run depends on type of cable/conduit and overfill.
Type UF cable at a 24" depth can be used without conduit.
Type THWN wires can be used in conduit at 18" depth.

Any splice must be accessible ...

Now here's something that puzzles me. I'm pretty sure that's true. But if so, why is it OK to splice direct-burial cable, but not to splice THWN inside conduit?

hmm maybe it has to do with the ability to pull out and install new conductors in the raceway. Or that it would be impossible to put a splice together within the pipe without doing it at an opening and pulling the splice through. Pulling conductors with a splice in the middle would be a good way to loosen the connection.

Phew, that's a long run of heavy gauge to discard, though. How about putting the meter on a pole where the mobile home was, and then running another length to the cabin?

"why is it OK to splice direct-burial cable"

Cause it is big and expensive to dig up an entire buried cable and replace it when it gets hit with a shovel.