You only need to protect the cable from physical damage, not nuclear attack. :-) Without seeing what you have, a 2x4 or two would probably suffice.

Next time you might want to think about some kind of rigid conduit and individual wires.

You can still run the cable in a piece of conduit (EMT should be adequate) for physical protection.

Put a bushing at each end to protect the cable from the ends of the conduit.

Fill does not apply to cases like this, so use any size conduit you want and can easily pull the cable through.

If you pull the cable back from its present termination and pull it back through some conduit without cutting the cable you do not even need junction boxes.