Invisible Objects?

I've not done any invisible object myself, however I think it would be easier if you play with the textures rather than touching the mesh. I've told this to Bakie before and it seemed to go really well for him.
What you need to do is the following:

1- Follow this tutorial HERE. You need to replace all shaders to phong alpha for the transparency to work. I'd guess that for the counter you would need to do the tutorial for each model and each part. (As you might know counters have more than one mesh depending on how it's placed in game.)

2- Import as a diffuse a completely blank image. That is a fully transparent one. For saving space, you don't need to make it as big as usual. A blank 4x4 image will be enought for you. I would make a transparent layer in Photoshop, export as .png and import to Studio.

3- Get rid of the bump and specular. For that do not delete them as a resource. Just blank the images and reduce its sizes. 4x4 for each will be enought.

4-Follow THIS to get rid of the OCCLUDERS the game could generate. I'm not sure if counters do generate them but you would have to check.

5- Lastly, if theres a shadow in the floor you would need to export the counter. Edit the uv for the shadow and make sure it's in a place where nothing is painted. If you run into this problem and need more help I can take some pics for you.

Warning: You might see the mesh completely black in the Studio model viewer, don't panic. Check in game and it should be transparent.

I believe this is the process Bakie followed in his invisible toilet and everything works fine.. I hope it works for counters too, if not, we could figure out something i'm sure Good luck!