The mix isn’t bad, it just needs some volume adjustments. No need to start from scratch. Have you tried mono mixing yet? That would be my advice in case you’re struggling finding the right balance. And I totally get that you want to get rid of the snare. What I was trying to say is, if you add some rhythm/rhythmic elements (sticks, clicks, whatever), you could “replace” the snare. But a kick alone combined with a too soft hat doesn’t do it. Even though it’s a different type of style, you could check Evigt Mörker for some inspiration in terms of getting rid of a snare. He usually doesn’t use a snare at all. Here’s an example:
Edit:
And keep your style! I really dig that kind of stuff.
made my day