There is no RFM file needed to see the cars in the game, nor there will be one for the server.
The veh files have the same class as the SWC-GT cars, you dont need to change that!
Please do not change the VEH files!
The rfm defines the category. If you have no rfm to a category, the car won't be available. And as you removed the default category and added the RDGTC-category, there must be a rfm or the cars are not available! Maybe you have an old rfm installed with that category so you see the cars. But we do not have one, so we either need the old default category in the veh or an rfm, otherwise there's no chance to use the cars.
Edit: Forget what I wrote above... I am wrong. The rfm defines the class, not the category...! BUT: Why did it work when I added the SWC-GT to the category? I had no RDGT Championship category, so I could not see the car. I added SWC-GT and my car was shown in the default Team Cadillac... (which is also strange^^). Now, I removed it and it works... I have the RDGT Championship category with my car in it... But now, I made the same with Brian's Mustang I am painting and it is not available! I added SWC-GT again, and it is still not available...I removed it again, but without success. Now I am a bit confused, because the veh file should be correct (I double and triple checked it...). Hmmmmmmmmmmmm... Strange...