I'd say that regardless of the effectiveness of recycling you shouldn't be doing it.

The (arguable) utility of your recycling vs. its cost to you is obviously very negative. And not just on purely selfish level: I don't know what your line of work is, but I'm sure society will benefit much more if you were calmer but didn't recycle than the other way around.

So here's a "get out of recycling jail" card for you and others like you. It's like herd immunization: Don't worry about it, we got you covered.