There has been no change from original COAS. To obtain a governor meeting to obtain a Letter of Marque, you must perform a bunch of quests for a single town mayor to boost his personal relation, just like COAS; doing the quests for a bunch of different mayors will take longer because the invite is based on the specific relation to a specific mayor. Such as find ring in the brothel, deal with thugs in the jungle, find nearby pirate and destroy/board, etc.
In COAS, your reputation will decrease if you board ships, even if the enemy. There was some modification in ERAS so that boarding enemies does not decrease your reputation as much, and it will actually increase your reputation if you have a Letter of Marque and the ship was a "war" type, which COAS did not do; COAS always decreased when boarding, even if patented. However, with a Letter of Marque in ERAS, if you initiate boarding with a non-war type, you will decrease if the enemy is a merchant and you take/capture (with a LoM in ERAS you should merely plunder merchants, then let them go...there will be no decrease that way. You are allowed to sink/capture war ships with a LoM and you will actually increase) and you will also decrease if you initiate boarding without a Letter of Marque, regardless of ship type, because you are not authorized to act on behalf of the nation yet. However, if the enemy initiates boarding, and you win, there is no penalty in ERAS. There should also be no penalty, but rather an increase if you are flying a nation and the enemy is a pirate in ERAS, whereas in COAS, it did not matter and you would get penalized for boarding pirates.
Also, just like COAS, your reputation will always decrease over time, each day, if you are above neutral and the decrease is higher for higher difficulty levels.