I don't know if this will help or not but I'll put it out there anyways. I have yet to actually fly in the spin and puke but my master's thesis was on a centrifuge-based tactical flight simulator being built by ETC corporation near Philadelpihia. You can check out the simulator at
www.etctacticalflight.com.
Anyways, for the thesis I had to take a ride in the simulator, and I experienced a lot of disorientation and motion sickness. After the ride was over I had to make a quick trip to the head to puke. My thesis at that point became a lot about what exactly caused me to feel this way.
You have various systems in your body which work to communicate sensations of motion to your brain. The two that probably communicate the most are your visual system (your eyes, duh) and your vestibular system (your middle ear). Now when these systems send different information to your brain about how your body is moving, you can experience spatial disorientation and motion sickness. This happened in the simulator because your inner ear felt and communicated to your brain how your body was actually being moved but your eyes, which could not see outside of the gondola that you were riding in, were telling your brain something completely different.
I believe that when you are sitting in the spin and puke, you can see outside of the cab that you are sitting in. The staff there gets around that I guess by making you place your head down on a table so you can't see out. There's probably another reason for this also which I will discuss in a second. Anyways, they can move you as fast or slow as they want and place you in any orientation that they want and your eyes won't be able to tell you the difference, although your inner ear may be able to give you some indication as to which way they are moving you. Eventually that information will be wrong, which explains why a pilot can become disoriented in the cockpit in low visibility conditions.
Now, after being accelerated in a certain direction, your inner ear will detect it, however, after a few seconds it will not sense the acceleration anymore until a new acceleration is placed upon you. This would explain why they have you raise your head up from that table it was on. You will experience discordant information about your motion from your motion detecting systems. Therefore, you will feel crappy.
There are a number of factors that will determine how you cope with these sensations. Physical conditioning, age, and probably most important, past experience, are some of these factors. So what I'm trying to say is it should get better the more you do it. I'm trying to stay really basic with this stuff. I got a lot more in depth in the actual thesis. I'm also hoping that I might be able to trick my mind into knowing how I am actually moving and not paying attention to my middle ear. I don't think this will work.
This is to help you hopefully understand more about what is actually making you sick. Definately follow the advice about the animal crackers and other stuff which should help you with the symptoms of motion sickness. Didn't mean to nerd out on everyone but I hope this helps some.