Are you using a pop filter or windscreen or anything in front of the mic? Maybe that could help filter out some of the super-loud plosive and fricative sounds.
Moving further away from the mic would definitely lower the volume, too (the SM58 is a cardioid mic, so it has proximity effect, where bass gets emphasized the closer you are to the mic). I guess the proximity effect will actually sound pretty nice on the kicks, but it also would explain why the peaks are so high.
I guess you'll probably need the compressor (or tanh if you like the distortion), but definitely give a pop filter/windscreen a shot if you haven't (and let me know if it works, because I really have no clue and I'm curious haha)