Sanhedrin 12: Rome's Impact on the Calendar

How far in advance of Adar -- when the month is added to the year -- could they intercalate the year? Rosh Hashanah time? Before it? Afterwards? Why would they to do it so early in the year? Only in a time of religious persecution, which the Gemara provides an example of, under the oppressive thumb of Rome. Plus, going back to the story of King Solomon's Temple and a monthly rotation that seems to have included the possibility of a 13th month. Also, if the majority of the people would be impure for the Korban Pesach, would that be reason enough to add a month? The Gemara presents several different ways of handling the situation, none of which is considered all that great. It speaks to the possibility of the leadership making errors, and then working that out.