Solar fry-by
Hi Jake
I reckon the best way to get out there in a hurry is via a solar-sail doing a near-solar swing-by. A fly-by slingshot past Jupiter and a plunge towards the Sun to about 0.03 AU, then the sail-force equals the gravity on the sail so the probe goes flying out of the system at ~230 km/s to hit 1000 AU in 20 years. About 130 km/s gets a probe to the gravity focus at 557 AU in about 20 years, which is slightly easier.
Adam