I've spent a bit of time today trying to find out how quickly (in terms of days) you can get through the current content. One of my findings has been that it doesn't seem possible to get any rules changes passed before the third board meeting, other than maybe by forcing Priti to allow you to take pictures of her, with all the penalties that comes with that.
My argument is that it isn't possible to gain enough money to either trick Priti or to get a prostitute for Mr. Wilson in time. In total either option costs 2700, you always need to pay 500 for the science equipment to get the keylogger for the first part of Wilson's quest and then you need either 1000 for the camera and 1200 for the clothing or 2000 for the prostitute and 200 for the viagra. You get 270 on the first day and you need enough money by Thursday of the second week to get it in time for the board meeting, which is only 8 school days. (2700 - 270)/8 = 303.75, which is way more than you can get from punishments on any day at such an early point in the game, much less something you can average over the first two weeks.
Since you can at most get one point from Wilson in time for the second board meeting (without coercing Priti) you'd need one from Potts and two from Chang. To get a point from Potts you have to teach her on every single opportunity. If you do the last lesson you teach her is on Tuesday and you can observe her class on Wednesday. However since she is unavailable on Wednesdays delaying by even a single day would put the last lesson for her on Thursday and you would not be able to observe her class, which is what gives the influence point, before the board meets on Friday. This means that the only evenings you can work with are Wednesday both weeks and Thursday the second week.
In order to get two points from Chang you need to hire her assistant, which includes several days of delay. In order to be able to pull that off in time you would have to tell Chang about buying the science equipment on the first Wednesday. This means you could not get Wilson's quest before the second Wednesday as both actions end the day. But if you get Wilson's quest on the second Wednesday you cannot get the keylogger before the second Thursday evening and therefore cannot call Priti to you office to steal her password before the board meets on Friday.
As far as I can tell the only way it might be possible to get the 4 influence required for any rules change would be to ignore Miss Potts and get all the influence needed from Wilson and Chang, which you can only afford to do in time if you save on cost by coercing Priti. Does anyone see any flaws in my thinking? Can anyone achieve it some other way?