Theoretical Neuroscience: what tools are in your mathematical toolkit?
Luckily, I think your list of requirements is already too long.
Your primary toolkit is going to be:

Linear Algebra
Probability and statistics
python

If you want, you can add:

Signal processing (filtering)
Machine Learning (mostly just applications of linear algebra)

I am currently TAing at an online summer school called Neuromatch Academy.  Check out their syllabus (3 week course) for an overview of tools useful in theoretical neuroscience.  homepage: https://neuromatch.io/academy/ syllabus, tutorials: https://github.com/NeuromatchAcademy/course-content
Out of interest, why NEF?  There are a wealth of frameworks out there, and NEF is relatively limited in its application.