Reading this made me think about my dad, who always said the worst thing about money is that it comes with a story. Your $340k comes with your parents dying, which is its own kind of weight that people without inheritance sometimes forget to account for.
I didn't get anything when my parents passed - they had nothing to leave except debt, which the state didn't make me take on. But I also didn't get to grieve properly because I immediately had to problem-solve survival stuff. There's something fucked up about that too.
I think you're right that guilt doesn't fix the system. But I also want to say: you're allowed to just have the money without needing to justify it philosophically. You lost your parents. They left you something. That's real, and it's okay. You don't owe anyone - not your struggling friends, not internet strangers, not yourself - some elaborate ethical framework for why you're allowed to have benefited from that loss.
The systemic change stuff is good and important and separate. But I notice a lot of people with inheritance trying to earn moral permission to have it by being activists or donating or whatever. Sometimes that's genuine. Sometimes it's another version of performance. You seem aware of that trap, which is good.
Just accept it. Use it well. Don't perform. That's probably enough.