"80% of the time, some bot swoops in and gets waaay more points than anyone else could possibly get"
If I understand you correctly, those aren't bots. Those are people. And if you're talking about the tournament positions, yes, it's luck of the draw, but also (apart from sp droppers) there are many players that spend hours on the game per day. You can't hope to get top 3 positions with such players in the mix, but sometimes top 6 is possible :-).
That said, I think this is unfortunately true of many games. There's a word game I play which has tournaments, and it's impossible to get top ranking if you don't invest hours.
If there was a way to separate casual players from dedicated ones, that might help, but offhand I don't think there is an easy way to do that.
Another option is to add some acoins as rewards for some of the other positions as well, or add self play challenges with acoins as rewards. The word game I mentioned does this. You don't have to always be a podium finisher in that game to advance.