Is is possible to export functions from a C# DLL like in VS C++?

Unmanaged Exports => https://sites.google.com/site/robertgiesecke/Home/uploads/unmanagedexports

DLLExport => https://github.com/3F/DllExport

How does it work?

Create a new classlibrary or proceed with an existing one. Then add the UnmanagedExports Nuget package.

This is pretty much all setup that is required.

Now you can write any kind of static method, decorate it with [DllExport] and use it from native code.
It works just like DllImport, so you can customize the marshalling of parameters/result with MarshalAsAttribute.

During compilation, my task will modify the IL to add the required exports...

I've seen people do this before, but it required ildasm, adding the MSIL .export directive, and then reassembling. A program named dll_tool can do these steps for you.

If you want to build a mixed-mode DLL with both native and managed exports, you should be using C++/CLI, which is specially designed for this purpose.