Welcome!

Generally though, I've found myself stuck here a lot because I enjoy arguing, and I like convincing other people to be less wrong. Specifically, before coming across this site, I spent a lot of time reading about ways of making people aware of their own biases when interpreting data, and effective ways of communicating statistics to people in a non-misleading way (I'm a big fan of the work being done by David Spiegelhalter).

Honestly that made me cringe slightly and I wanted to write something about it when I came to the second paragraph:

I suspect that I'm pretty bad at overcoming my own biases a lot of the time. In particular, I have a very strong tendency to believe what I'm told (including what I'm being told by this site), I'm particularly easily inspired by pretty slogans and inspirational tones (like those this site), and I have, and have always had, one of those Escher-painting brains, to the extent that I was raised very atheist but am now not so sure. (At some level, I have the thought that our form of logic should only apply to our plane of existence, whatever that means.) But hey, figuring all that out is what this site's about, right?

You are bad at overcoming your own biases, since all of us are. We've got pretty decent empirical evidence that knowing about some biases does help you, but not with others. The best practical advice to avoid being captured by slogans and inspirational tones is to practice playing the devils advocate.

I'm also quite fond of listening to economics and politics arguments and trying to tear them down, though through this,

Check out LW's sister site Overcoming Bias. Robin Hanson loves to make unorthodox economical arguments about nearly everything. Be warned his contrarianism and cynicism with a simile are addictive! He also has some interesting people on his blogroll.

I've lost any faith in politics as something that has any sensible solutions.

I'm afraid hanging out here probably will not make it any better. Seek different treatment. :)