"Many of the links posted are outdated, and most of the material that still, well, exists online, is purely theoretical and mostly limited to "how to draw this line". "
Well, that's generally how you implement anything. You read material that explains the general methods you use to create a software renderer. Then you implement it yourself using the programming language of your choice.
The algorithms, math and underlying fundamentals haven't changed since the 90s. You could read about software rendering from 1990 and from that using your modern programming language and modern single and multi-core parallellism as well as GPU implement the very same thing, just more in parallell. That particular aspect might not be very interesting for you though, so if you want to keep it simple - stick to the original methods and try to understand them well.
Anyways, I googled for 5 mins and found a C# tutorial series:
A more detailed series here:
Also, keep in mind that if you are looking for strictly C# code, you are going to have a bad time. You really need to be able to learn from and understand articles that explain things from a more academic perspective, that explains things in terms of algorithms, pseudo-code, algebra (and unfortunately sometimes logic.)
To make a software renderer you might want to make sure you have covered at least the basics in linear algebra first.
I wanted something a little bit more advanced than just drawing a line, because I don't really know how to properly scale this line into an entire scene, and I'm looking for something on a larger scale.
The thing is, it's a school project, and the requirements are either Java or C#, and no OpenGL or DirectX. The first link uses WPF (which uses DirectX for rendering) and SharpDX.