Josephus, in Jewish Antiquities, once suggests that Judas Maccabee, the brother of Jonathan, held the office during this period; Judas had in fact already died.
A vacancy in the high priesthood through these six years is indeed highly unlikely, if not impossible. In religious terms, the High Priest was a necessary part of the rites on the Day of Atonement - a day that could have not been allowed to pass uncelebrated for so long so soon after the restoration of the Temple service. Politically, Israel's overlords probably would not have allowed a power vacuum to last that length of time.
It has been argued that the founder of the Qumran community, the Teacher of Righteousness (Moreh Zedek), was the outcast High Priest of the inter-sacerdotium. In this view, his name was wiped out by his Maccabean successor, supported by both the extant records: the Books of Maccabees and Josephus (who claimed kinship with the Maccabees). This view is based on sources from the Qumran community, that however do not spell out names or events clearly.