I apologize because this is not really an answer to your question, but it was getting too long for a comment.
I think the problem is that you stated in your question that you want the titles to be centered "perceptually." There may be a more specific definition of "perceptually" that I don't know, but the way I read that it means that the titles should LOOK balanced, whether or not they actually are balanced.
As @Webstarian said in the comments, all kinds of issues impact our perception of balance in design. Darker colors recede, bright items can appear larger than they actually are. Like Webstarian, when I look at your pie chart, the maroon slice appears really bottom heavy to me--to balance that, my gut says to pull the label up higher and to the right, even though that is completely out of the range of your algorithmic guides.
I can't speak for what algorithms are used in high-end software programs for determining where labels should go--but I use Adobe's InDesign frequently for layout, and they have layers upon layers of tools allowing you to tweak the location, spacing, slant, etc. for every single item you place on a page, for the individual letters in a sentence, etc. And the reason they offer that level of adjustment is because I don't believe there is any way for a program to account for all of the "tricks" our brains play on us when the information that enters through our eyes gets interpreted by our brain.