EUREKA Franz! I think I got it all figured out:

At the moment the # of points won and lost in a match is equal and based on the overall rank.
Example: HHC vs Nino in elite:
HHC wins:
1122 + 55 = 1177 HHC rank
1483 - 55 = 1428 Nino rank
Nino wins:
1122 - 24 = 1098 HHC rank
1483 + 24 = 1507 Nino rank
What might make things interesting is using both the overall rating
and the season rating to calculate win and lost points. And apply a different counting for both players:
For the winner:
WINNER = Season rating
LOSER = Overall rating used
For the loser:
WINNER = Overall rating
LOSER = Season rating used
Suppose me and nino have just played our first game of the season. In this case our season rating is naturally 1000 pts. The points would be calculated as follow:
HHC wins:
HHC rating change is based on 1000 for HHC (Season) and 1428 for Nino (Overall): HHC gets roughly +63 points.
Nino rating change is based on 1122 for HHC (Overall) and 1000 for Nino (Season): Nino gets roughly -36 points.
Nino wins:
Nino rating change is based on 1000 for Nino (Season) and 1122 for HHC (Overall): Nino gets roughly +36 points.
HHC rating change is based on 1428 for Nino (Overall) and 1000 for HHC (Season):
HHC gets roughly -20 points.
As you can see, in each match the number of points won and lost isn't equal anymore, but I don't think that's a problem.
The real advantage here is that:
A) Every season everyone will start out the same again. Having a high or low rank will not affect the number of points you get for beating someone. (Random with an overall rank of 1556 and Sillynoob with a rank of just 245 will both receive the same ammount of points for beating HHC, as both of them have the same season rank (1000)).
B) As the season progresses the best players in this particular season will get less points for beating an opponent than someone with a lower season rank (this keeps players from accumulating ranks into the 10.000's, instead überactive players will reach a certain ceiling, where any additional wins hardly give points, while losing games deducts plenty).
C) Most importantly, at the start of a season, beating noobs gives you way less points than beating veterans, even though their seasonal ratings may be the same.
To summarize, this solves everything:
-> a fresh start each month
-> history has no effect on your chances in this season (for good or for bad)
-> no newb bashing
-> being active alone isn't gonna cut it, you need a good record as well
Surely this can't be too hard to code MI?
This system seems pretty solid to me