"Problem resolved."
Apparently, it seemed (as ahwulf said, and I suspected) that my project paths / libraries / headers were somehow corrupted inside Xcode 5.
What was my decision? After additional tests, I just physically removed some of my apparently conflicting libraries (testflight, flurry, etc.) from the project (and ALSO from disk) and started compiling, waiting for obvious compilation errors to appear.
When they appeared, I just added the files. Xcode asked me to add (one file / library at a time), and then one by one, all these errors started to disappear slowly. My original binding error ALSO disappeared, so my project is under construction again.
I have a feeling that I really don’t know what I did, but "it worked."
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