[skykooler]

650 AU is quite far away. To get there in a reasonable time frame (a few decades), you have to be going quite fast, on an escape trajectory out of the solar system. If you wanted to be on an elliptical orbit, the orbital period would be over five thousand years (and a circular orbit would be over sixteen thousand years). It's so far out that it's just not practical to try and move laterally.

The other nice thing about being on an escape trajectory is that because of how gravitational lensing works, rather than a focal point you get a focal line. So as the probe continues moving away from the sun, it can continue imaging its target (and the image quality may get better as it gets further out, since the ring gains more separation from the surface of the Sun.)