Have you tried remapping the key with the game's built in key-mapper tool? Make sure that you don't use the emergency break (by default its keyed to "z") and instead use the handbreak.

Yes, I've used the key-mapper and I think I have it set up correctly. Currently the controls are like this:
Accelerate: W
Break: S
Steer Left: A
Steer Right: D
...
Emergency Break: Z
And then I use the S key and I get the jolting. With mouse up/down for Accelerate/Break it behaves differently and I can control the throttle smoothly.

The answer is NO. It's nothing wrong, it's just how it is for any game. Unless you're playing a plane or spacecraft simulator, there are no buttons assigned for adjusting throttle. You have to use mouse or a controller with axis support. Period.

Now please mark this post as "answer", so it won't show up in the forum as orange/unresolved. That's my only reason for necroposting on this thread.

- Sam