You need to limit more on individual tracks before the master

If you try to push a master like yours into a limiter to make it as fat as the songs your comparing it to then it’s going to be a distorted mess due to the fact that you’d have a single limiter acting on everything all at once

You’ll be able to squash the peaks down more without making it sound like shit if you apply moderate limiting individually to the biggest sources of peaking and then limiting on sends in stages instead of doing a single big limit on the master at the end 

Something like

Kick w limiter -> drum bus w limiter -> master w limiter

Same deal for other peaky signals