I disagree. I think all the factors you are concerned about can be eliminated with a large enough sample size, like in the thousands (or maybe 10s of thousands).
You allow each person to select the genre of music they like, and you play a few clips from a few songs of each bitrate. Then they guess which is 24-bit and which is 16-bit.
I'm not paying to set it up. But it could all be done online without too much grief. It would be good to track the other statistics (age, headphone brand, etc.) as well, and see if something falls out of that.