After all of that work, good places will take a chance on you; then show them they were right to do so.
One piece of advice: Even if you think your C++ and Python are beyond beginner, I would recommend going through a C++ book (http://www.amazon.com/Primer-Plus-Edition-Developers-Library...) and a good Python book, if you haven't already, just to really refine your style and be aware of how to use the STL properly. Standards and practices matter a lot when you're a good Software Engineer.
If you do all of that, you'll be better than 70% of the people calling themselves "Software Engineers".
FYI. I'm a Software Engineer and my degree was in Linguistics and Literature.
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