At last, Results!
The code is written in Python, with the bits that need to go fast (numerical integration and root finding) compiled and optimized for the local CPU flavor. The optimized functions were supplied by the wonderful SciPy project. Given how much work I put into this project, I probably could have done it without SciPy, but I wouldn't have wanted to. The end result would have been much less reliable, slower, and more annoying to use. I am also extremely grateful for the Debian project and its package maintainers, who deliver the only OS I can find that has all the necessary packages compiled and ready to use.
Now, I just have to prepare the cases, run them, and write the "Conclusions" and "Error Analysis" section. That, and cross my fingers and hope that I don't get any grumpy reviewers.