LeftHandofGod (Well, I can always just do this...)
Erujan looked at the debris field - one more method of solving this.
He then sprinted as fast as he could - to the navigation console, the control of the drive cores. He swiftly maneuvered his ship with the warp drives, near the debris field's trajectory, and close enough to form a slipstream rift. In just one second, his brain calculated a short slipstream jump... He hoped that Kaavex will forgive such a waste of FTL fuel.
In just two seconds, a tear in space and time opened up, the placement ensuring the debris will enter, and a purple glow of energy came from the slipstream rift, linking to a portal on the other side of the ring.
...That will place the moving debris cloud on a collision with the star.

(i guess it would look a little something like this)
(If it were an actual dyson ring instead of a ringworld, I wouldn't even need to use the slipstream rift - I would just tell the CRCKI to move whatever dyson ring habitat out of the way and shoot at the task force.)