I raised a Developer Technical Support ticket with Apple about this, and spoke to the Xcode engineers at WWDC.
Answers to my own questions
how do I configure build settings so that a project with a nonstandard build configuration name (like LocalRelease) can depend on other projects that use only the standard build configuration names?
Answer: cannot be done.
is it in general a bad idea to introduce additional build configurations because they do not allow smooth interaction of dependencies between projects in a shared workspace?
Answer: yes, this is a bad idea.
So creating a new named build configuration is not the smart way to do what I was trying to do. Unfortunately, seems like the "simplest" solution is to embrace xcconfig files and change config files manually for this sort of thing.