Hard to imagine that the ratings will ever become stable, when gaining or losing 60 points in one game is considered normal.
Cheating in Teams Mode

I think it is probably just a new normal for 4 player that the ratings are going to deviate at least double then normal chess. *maybe 4 times. if we start seeing that as ok and normal then it should not be a problem

In Teams the rating changes are moderate. It is possible to make them moderate in FFA too, for example, just divide by 3.

@Renegade_Yoda we could use this approach to solve almost every human problem. If we start seeing war, poverty, cancer and natural disasters as OK and normal then we could live happily ever after!

@skeftomilos lol your right and we just solved world peace by moving the bar
*and I thought that would be a tough one hehe. As for my thought... I could be off here but was thinking that in normal chess you are the factor in win or loss. But with 4 player there is a multiple factor of more? in FVF its x 3 in partners at least x2. That factor to me was a possible reason for ratings to naturally move up and down more then normal chess. So I was thinking acceptance of a new game new system makes sense instead of trying to plug it into the old norm. Probably off here and that would not be the first time

Comparing standard chess with 4-player chess, I think that the playing strength of a player is more determinant of the game result in standard chess than in 4PC. This means that we need more 4PC games to become confident about a player's strength than we need in standard chess. So the rating changes should be smaller, not larger, compared to what is considered normal for standard chess.
Some instability in a new and rapidly-expanding rating pool is entirely normal. I would expect that to settle down in a few months.