The six month clock starts on the date the preferred is purchased and continues through conversion. In other words, the clock does not restart at the time of conversion so it shouldn't have any effect on when holders choose to convert.
Although true to form there is another discrepancy in the filings...
According to the filing the preferred holders do not become shareholders of record (of the common?) until the date of conversion. As I am not and do not claim to be a securities attorney, I have no opinion if it means the clock starts then or not.