I don't know, but Jupiter has that kinetic energy now, and if you slow it down until it falls into the Sun, it won't have it anymore. The energy has to go somewhere.

Maybe you scoop up big balloons of gas, slingshot them to Mercury with a tether, catch them with another tether on the dark side of Mercury to decelerate them (thus generating electricity which you use to make some kind of fuel), and toss them Sunwards from there.

Or maybe you use an electromagnetic mass driver in the Asteroid Belt to launch an unbelievable number of small rocky masses to a gravitational slingshot around Jupiter back to the same mass driver again, but at a higher velocity, so they generate electric power when it catches them before launching them again. Each mass goes through this circuit tens of thousands of times.

There are lots of possibilities.