The next article about the convoluted build configuration automation model (EnvDTE/EnvDTE80) and its diagram series of articles that I have started shows the code to add or delete solution configurations from a Visual Studio add-in. The deletion approach of the automation model has a hidden trap explained in the article and code:

HOWTO: Add / delete build solution configurations from a Visual Studio add-in
http://www.mztools.com/articles/2013/MZ2013008.aspx