[logfromblammo]

The radius of Sol's gravitational influence is much larger than the radius of its coherent mass.

The sun is always at one focus of the elliptical orbit. You just can't get the orbit close enough to plasma-brake near perihelion without also pushing your aphelion way out. So you have to aim away from Sol in order to get there at lower energy. Basically, a Voyager probe that stops at the very edge of the gravity well and then plunges straight down. Spiraling down while decelerating is faster, but costs more energy. But as you get closer, you can harvest energy from the solar wind and solar radiation, with solar sails, so the amount of delta-v you have to load onto the launch rocket does not represent your entire delta-v budget.

There are ways to trade off time for delta-v, but at that scale, the ways that really make a difference mean that the person that sets them in motion will be ancient or dead before they finish.