The fact that your material says baked, means that you are including blender nodes which have no direct translation to BJS’s PBR material. First, give a screen shot of your materials which are baked. Changing them over to Principled shader, will probably fix. Something as simple as solid colors should be not to big a deal.
Also, while the exporter attempts to bake materials, another reason to avoid them in production code shows in your very example. Baked materials cannot be shared across meshes. If you have a material that in Blender that has no direct translation on 3 meshes, then it will have to baked 3 times. This is not scalable on the BJS side either.
Also, there is a log file generated. I kind of require it be posted.
Looks good. Now you see a lot of registered as also a user of Material: x messages in the log. So they are being re-used. Not sure what those _baked things are. They are not in the log file. If you opened up the .babylon in Word or NotePad, does a find of _baked get a hit?
I also tried it again with blender default cube. 2 materials placed on it, a smart uv project and the faces triangulated. No more. Then exported. Here too, the first material is renamed to _baked. Blender 2.8 (.75) and the babylon exporter 2.2.3
I have the same problem and rely on on the material name. The first one is always “baked”. I have then to rename it in the file itself. Is this solved?