This reminds me of something I heard, somewhere. A non-native French speaker was in France and having trouble making themselves understood. For some reason, probably out of frustration, one day they tried putting on the hammiest French accent they could muster, positively Python-esque parody of French pronunciation and verbal mannerisms. The story goes that this solved the problem, people understood them perfectly.
What I got from this was that maybe hamming it up can help you throw more of yourself into the material. Easier said than done, but probably an interesting exercise to exaggerate the vocal inflections just a little and try to get closer to 'the vernacular'.