If the only rules are "only accelerate away from the nearest star", that doesn't preclude using a planetary gravity field to also adjust your orbit.
E.g. Making small course corrections in interstellar space (or simply mission planning exactly enough) so that you hit a planet's gravity well on insertion into the destination solar system, thereby slinging yourself into a more manageable eliptical orbit (and potentially burning something else at the right point to change your orbit)
I'd also be really curious on how something like this works in the area of interaction between a planetary magnetosphere and the "sail" (e.g: https://en.m.wikipedia.org/wiki/Magnetosphere#/media/File%3A... ). Looks complicated!
You’d probably just sail on past, with a deviation in course, but not orbit or a 180. For any gravitational maneuver, you could rely on momentum and shut down the drive, restarting for the return leg.
(full disclosure: never played KSP)