I am the developer of the Altium2KiCad converter.
The converter is currently able to handle most of the files, not just BunnieĀ“s files. Most schematics are converting fine, the 2D PCB layout is nearly done, the 3D PCB is still work in progress.
If anyone finds files that cannot be converted with it, please let me know.
I was recently given a converter for STEP->WRL files which I will try to integrate soon, which would replace FreeCAD in the conversion process, that should make the whole process much easier and fully automatable.
I was thinking about offering the converter as a web service, if it is really too difficult for people to install and use it themselves.
I would appreciate any help and feedback, if you notice anything that could be converted better.