"if one team had one single chance of calling for a replay, it wouldn't kill the dynamic, but would solve the problem of nonaccredited goals or the Kaka situation with Ivory Coast."

This is roughly the system employed by the NFL, and it works fairly well. Coaches can challenge a number of calls per game (2, I think?) and are penalized with losing a timeout if their challenge turns out to be invalid. I don't know if there is an equivalent penalty that could be leveled at a soccer team for an invalid challenge.