Hi ishuku,
I would start by wetting the soil and letting that sit for awhile. Then, take the dracaena out of the rectangle pot and begin to shake the soil off. As you do this, untangle the roots as you go. Once you get an untangled view of the roots, you can see which roots can be trimmed back. It won't hurt the plant to trim the roots. Don't trim out more than a third and leave a well balanced clump. Replant directly into the new container adding fresh potting soil and don't forget to water again at this point. Think that should do it.

ishuku, I'd decide where I want to cut the roots on the long side of that L.
I would use a sharp knife or heavy scissors.
I would cut straight across the container; and not worry if I do not get all the roots.
Leave the plant in the container long enough for the cut roots to start branching. Addition of organic matter in the form compost in the area of the cut roots will help this process.
Monitor the root branching progress; and I would guess that after about 8 weeks, you will be able to lift the plant with its smaller root ball, cut away any remaining long roots and set it in the new container and add more compost to set it firmly in place.
It is similar to root pruning a field grown tree; a quarter circle (12 o'clock to 3 o'clock; 3 to 6; 6 to 9 etc) at monthly intervals. New feeder roots proliferate inside the pruning circle so that when the whole tree is lifted and set in its new location, the shock is minimized.

Can we see a picture of the plant? If you time things right & have a plan going in, plants will tolerate an amazing volume of root reduction.
Note:
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I'd be thinking about bare-rooting and getting the plant into a fast-draining, well-aerated soil when you do the repot.

Al