I’ve found that custom molded in-ear hearing protection combined with industrial ear muffs is the closest I can get to drowning out nearby conversations (including loud ones) without requiring a layer of music on top or bothering with headphones underneath the ear muffs.
I've been considering this as well, but it'll get really uncomfortable over the course of a day. And then you have the colleagues who think they can just interrupt you all the time, with minor questions. Or the ones who just hover around, waiting for you notice them.
Careful with this. I have tinnitus (arguably from 8 hours/day of headphone use), and when I doubled up as you described, my tinnitus became unbearable because it was the only thing I could hear and my brain "latched" on to it. I'm still trying to train my brain to stop listening...
Now I wish my work wouldn't suck so I could actually use all the focus I get this way :)