Pitts pilot reported striking a runway turn-off marker after losing directional control on landing roll.

Narrative

On returning from a local training flight; I was assigned [a west runway]. On final; the winds shifted from 'variable @ 3' to '020 @ 11'. I took note of the crosswind; and proceeded to the runway threshold; following a slower-moving Cessna 172. After the Cessna had cleared the runway; I touched down uneventfully at around the 1000 foot marker and proceeded to roll-out. At first; with some left rudder; the aircraft rolled straight. But it soon ran out of rudder (even fully deflected); and we were 'headed for the weeds' - at the right edge of the runway. After briefly striking a turn-off marker; the airplane turned back to the center of the runway; and I exited to the ramp. Very simply; in hindsight; with the wind-shift; I should have abandoned the landing; gone around and requested [the north runway]. (It is never a good idea to land a Pitts with a quartering tail-wind.) I'm grateful that no serious damage (or worse) resulted to me; to anyone else; or to the aircraft. (The sign is of a 'break-away' type; and; fortunately; minimal damage was sustained by the wing tip.)