How can I get bulk riser cable back into the box?
Don't

Just coil it up and tape it to the side of the box. Then put the box away, or sell it, depending if you have any future need for cable. The coiling interior to the box to make them work is more complex than it appears on casual inspection, and getting the box tangled so it won't "just pull out" is far worse than having some coiled cable on the outside. How do I know? 300 feet of miserably tangled cable in a box that I had to fight with until I used it up, got a new box, and NEVER tried that foolishness again. Network wiring is part of what I do for a living.