Haircut at the End of the Thirty Days During the Three Weeks

An Ashkenazi mourner for his deceased brother, whose thirty-day mourning period ends during the Three Weeks when haircuts are prohibited, is he allowed to be lenient with haircuts?

Shulchan Aruch, Orach Chaim, Siman 551, סעיף 15: "One who is overtaken by mourning for the deceased and Shabbat, and his hair has grown heavy, may lighten it with a razor but not with scissors; and he may wash his clothes in water, but not with niter and sand." Mishnah Berurah, Siman 551, סעיף קטן 87: "This is only if the thirtieth day falls in the week of Tisha B'Av, but if it falls earlier, it is permitted to cut hair and wash clothes, even though we usually prohibit this, here it is allowed because he is overtaken by mourning, so writes the Taz in the name of the Bach, but the Aruch HaShulchan holds that one should not be lenient unless the thirtieth day falls before Rosh Chodesh, and so write several later authorities."