So in my attached .blend file, (I have also attached .jpgs of my original design for you to see what I'm trying to model) you can see that I have two separate meshes. I can bevel the bottom one properly, but the top mesh cannot be beveled; this is most likely due to bad geometry on my part from creating too many of the top faces and crevices with curves (please note that no booleans were done on this model). I've already done a quick and dirty way of making all the faces into tris and quads with a few clicks from a youtube video tutorial. But of course that didn't solve the problem either; it still didn't bevel (likely due to the tris).
Should I just go in and manually change all the ngon faces to quads? And even then, would that truly make it possible to bevel, or would I just be wasting time? Is there a faster way that I just don't know about, or is this unsalvageable? It's the only option I can think of at the moment besides relying on the Bevel Node, which I'd rather not as I want to solve the root of the problem and not just hide it with a node.