Alternative rating.

1). Couldn't it just replace the rating? Or maybe let there be two for now.

Last time, it wasn't possible to change it, so now I'm only aiming for the second, alternative option. Besides, it's difficult to find seasonal winners using this system; let the existing system determine the seasonal winners.

3). Why not make it a double bonus in tournament play? So, a tournament victory would count as two (I've already written about this).

The same applies – this is left to the existing rating system. The alternative system only considers pure skill, without bonuses for tournaments and the number of games played.

4). Also, if people don't play in the tournament or withdraw from it, you could simply deduct rating points, even if it's not a large amount. And don't make a distinction between a valid reason or not.

No, players who don't care about tournaments might also not care about their rating.