Copying those files should not be the issue. I did that as well, and have had no strugles.
I know it's a bit of trouble, but if you really want to exclude any hardware other then the PC and the installation, you need to take that PC to a friend, and plug it in his internet. Doesnt matter if he plays Race or not, you just need a connection.
Is the issue related with the number of cars on the track? If it's a connection issue, it's most likely that if you start on a empty server, it runs more smooth then on a full one. You could try that as well.
How does the start go when you play an online race? Is it more terrible then, compared to let's say 1 lap out when the field has spread a bit? Or is it that even alone on a piece of track, there are issues?
What happens if you set the visual settings down a whole lot? Does that matter? I believe Dedicated servers "just" synchronize the game, and do not send graphical data around. So, changing the detail should NOT make a difference when the issue is connection related. If it DOES change the smoothness, I can't come to another conclusion then the GPU, which seems weird since offline all goes well...
Just trying to pinpoint the cause of this issue. All in all it's a real brainbricker....