Well, I know this game is going to end soon, one way or another, so I will try to give my last lecture.
This point of a game is usually what people call "end game" and it´s the point were people look (or should look) for the best result that they can get. Usually the powers could be in three situations (four if you include the dead ones, but in this case you have nothing to do but look ):
1)You are a small power (usually aroung 3-4 centers, but maybe even 1) - In this case you need to find a way to be usefull in stoping someone´s solo. Sometimes this include helping the biggest guy around so he turn so big that everybody have to unite to face him. You should look closely for the possible stalemate lines that can be formed and try to find a way to be part of it. For example, if you are England, having Nwy and/or Stp is a great way to be alive when the game end. Same is valid for Mun/Ber as Germany and other key centers for the other nations. Try to make to risky for anyone to kill you. You should use tactics but also a lot of diplomacy to avoid beind eliminated just to have a smaller draw. Not an easy task when you have some greedy players or a high pot (points or GR pot....)
2)You are the big power (or one of the big powers) - Well, in this case you have usually at least a draw guaranteed, so it´s time to find a way to get a solo. You should know what are the 18 dots you need (if you don't know you have done a poor job in the middle game) and need a plan to take them. Problem is that probably the other players also know that and will not make your life easy. So, put tactics aside and work on diplomacy. Try to explore the grudges between players and also the small nations that will usually do whatever it takes to survive. Don´t shorten the player pool (this is where sometimes people make big mistakes). It´s a lot easier to try for a solo with 6 players alive then with only 3, as the coordenation needed for 5 players to stop a solo is a lot harder to achieve then between only 2. Having a strong knowledge about the stalemate lines will help too, so you can avoid it´s formation, focusing on getting ahead of them not on grabbing centers.
3) You are a medium power (this mean you looked at the board and see you have 0 chance of a solo but have also small chances to be eliminated) - In this case your task is avoid someone getting the solo. That should be your first goal, not having a n-way draw. Of course you want to be a part on a draw, but you should look the board aiming to avoid a solo and not trying to get the smaller possible draw. Of course, usually a 3-way draw is better then a 6-way, but both are far better then a survive (assuming you are playing WTA, that is the only way to play for this professor). So, if you need to keep alive that player that stabbed you twice or the other one that has only 1 center to secure the draw, do it, don´t risk it for vengeance or greed.