Something of interest: Jeffery's interval. Using the lower bound of a credible interval based on that distribution (which is the same as yours) will probably give better results than just using the mean: it is handles small sample sizes more gracefully. (I think, but I'm certainly willing to be corrected.)

I recently did a similar thing for ranking vendors by feedback, using both a Jeffreys interval and a Wilson interval; even on the vendors with little feedback, they were overall pretty similar. IIRC, I don't think they differed by more than 10% anywhere.