Wow, that sounds tasking. Don't get caught in the knot! Keep a breathing hole in there.
What I might do, ... I hope I never have to:
find the longest straight distance in your appartment.
Place the yarn roll on one end and unwind the double strand all the way down to the other end of the room, the hallway or whereever you are.
Now go to the end and start with one end. Make it a nice tight coil.
While doing that, keep the other end that you are not winding tucked tight at the end you pulled it to (place something ontop, make a slip knot or something...)
The strands will be twisted together so you may need to grab around that strand a few times to untwist them. Do you know kite flying with double lines? to find out if things are really twisted or just a little you seperate the lines on the open end as much as your arms allow you. That moves all twistst to one end and you can roll a bunch before you even have to deal with the untwisting.
When you have reached your yarn cake you put that ball down and go back to do the other end. That is now a straight roll-up-job.
Then you start over again.
That will be work, but it remains un-entangled.