No, K-factor won't have any effect on the mentioned problem - it'll just raise the rating, both overall and seasonal proportionally. Well, it might help somewhat for one season, but the seasonal rating will just catch up and you'd have to change your K-factor every couple of seasons and will give a massive rating inflation.
Rating calculations usually involve a logarithm. It determines your chance of winning (or rather, how many points you'd statistically win in a game against player B).
For example, in chess, your projected winning percentage against someone with 400 points lower than you is 1.0 (ie, you win all the games)
The best way to suppress noob bashing and activity playing too big a role (while maintaining the current system) is just to make the rating range (of 400 in the example) smaller: that way, you won't score any points against someone with 300 points less, rather than against someone with 400 points less.
You'll also gain your seasonal points faster, because the upper limit is also smaller (you win the same amount of points against someone rated 300 points as you would in the old system against somebody with 400 points higher).
But there's a trade-off if this happens: ratings will fluctuate more than they used to and ratings will become less reliable than they are now.
Setting a roof on your total amount of games also has a trade-off, though: avoiding.