TwentyFourteen: Set featured content to be random?

I’ve got a bunch of posts of artwork by different artists that I’ve uploaded and I tagged each of the posts as a month (i.e. “january”) so that I can set the featured content for a specific month. This way, each month 6 artists are featured on the homepage.

I’d prefer to set this to be random, so that each time the browser is refreshed 6 new artists appear on the homepage. Does anyone have some coding skills to instruct me on how to do this? I’m assuming that since I already tag each post as a month that I could somehow tell the code to randomly select a month, but I don’t know if this is the easiest solution.

http://www.capitolboxart.com

Thanks!