Also ditch the rear bumper, it's a chunk of unnecessary weight that works on the pendulum, if you want the rear to stick you need front weight not rear weight.

Also look to be missing the screws in the rear arm mount up front.

And the rear too.....

while a fun car to drive its best just to replace the chassis and all the a arms and upper control arms. start fresh. that should resolve all your issues. these cars have a tendency to clap out over time. nit sure what rules u have to follow for racing? however we run spools and tamiya oil diffs

First of all let me say thank you so much everybody for your quick responses!
Sorry about the missing screws. I had chassis brace I printed that I took off to make sure it wasn't introducing tweak. The problem persist with the screws installed. This car is far from clapped out. It doesn't even have two packs through it yet and it hadn't been crashed until my latest test run, I traction rolled flinging it around trying to assess the handling on my hill. Oops! Before that it's only been on the track one time and it let me down and I parked it. I thought it was due to the shorty pack upsetting balance but it wasn't. This car is typical to me cheap car sloppy, but sloppy never really makes a whole lot of difference in my experience. I've spent hours and hours shimming things on other cars to perfection only to have them drive the same. You probably wouldn't believe my shim collection if I told you. The rear diff grease is extremely light, if I spend one wheel in the back they will counter rotate for almost 1 second. I would call it more lubed then greased up. I enjoy loose rear diffs that keep the cars from stepping out because they unload the inside tire. Interestingly after that roll which was not wimpy and I didn't have a body on it it now has zero degrees camber on the front right and the same 1.5 on the left front. I gave it a huge bunch of twists both ways and the chassis doesn't seem tweaked I think I bent the knuckle.
If it really needs a new chassis and new arms already I'm over it. The guys that are racing these crash like crazy, but I've never driven their cars and most of them don't have a ton of experience, they may not care/notice about different cornering left and right. When I'm watching The other guys it does seem like when they corner hard and get on the gas early it can get a little sideways or a lot sideways both ways. Even a Scandinavian flick will barely make it spin to the right.

Here's the behavior. Grrrr.

Here's the behavior.
Before this run I swapped tires and shocks locations, as well as swap the rear axles side to side, and hexes front to rear rear to front. Grrrr.

In my experience these cars tend to unload the rear too easily in a lot of situations. I realize that doesn’t help determine why yours is doing this in one direction but not the other. I typically run Tamiya stiff springs in front and medium in the rear. Try adding some internal limiters to the rear shocks to see if that helps. I didn’t catch it in your original post but do you have a bearing kit in the car? I’m wondering if using the stock bushings you’re getting some weird binding under the weight of cornering…but just throwing ideas around. These cars are barely more than toy grade, and I say that as someone who loves the tt02 for what it is. Sometimes they just behave a little funny and you have to find ways to compensate, maybe just bumping up the ride height a hair on one side if it helps, or dialing back steering in one direction to prevent oversteer, even loosening up bulkhead screws or steering rack screws a smidge. I’d take it back to the track to run it on a prepped surface with prepped tires and just spend some time figuring out how to get it driving to your liking.

One more thing, you’re not using the stock servo saver right? I can’t tell for certain in the photo.

Did this rear stepping out just start happening?
Shaft driven cars are know to have on power torque steer due to the nature of rotating mass and the way the TT02's diffs are setup.
Also the Traxxas 550 motor is very torquey down low, maybe tune your radio for more negative expo?

My guess is the 12T motor is amplifying a behavior that isn't as bad with less powerful motors.

Your throttle inputs have to be way smoother than that, and you need to test the car on a prepared track surface...Also try a little bit of chassis rake: front 5mm rideheight and rear 6.5mm...

I appreciate you guys responding!
I completely understand about the throttle inputs. I'm only going so aggressive to show that it simply doesn't spin out to the right no matter what I do. The spin-out problem makes itself known on the track in tight corners with smooth throttle on exit and in fast corners on the edge of traction. I can't carry nearly as much speed to the left without spinning out as I can to the right. I've run VTA with some state champ VTA guys and I do okay, I'm definitely able to drive the car properly during a race.
I do have a bearing kit in it and an aluminum servo arm. I used shoulder screws and washers to get proper drag arm alignment with the servo horn.

It is possible this is due to the Traxxas motor and the torque coupling, but I have plenty of other shaft drive cars of different scales with brushless motors and I don't see this pronounced an effect.
These are definitely just a step above toy grade as far as sloppiness I agree. This isn't a knock on Tamiya, my very first car was a grasshopper in 1985. 40 years later my daughter got to build the same kit!
The class I'm racing this in is a plastic tub chassis class. We all run the Traxxas 12 turn and yokomo 28A's. Outside of that there are no rules. I just ordered a yokomo RS 2.0. it's the most traditional four-wheel drive belt touring car I can find with a plastic chassis. I have a feeling this is going to make all my tto2 problems go away. 😉

Which TT-02 kit? What upgrades or hop-ups on the car?

Couple of things come to mind...
- Did you use trim or subtrim to center the steering servo? Are you using adjustable turnbuckles on the steering?
You may not have centered your steering properly either mechanically or in the radio which might be giving you too much turning. If your radio supports, check your EPA (end point adjustments). Also you want to use SUBTRIM to finely adjust the servo as using trim can cause more steering in one direction vs the other. If you only have Trim on your radio, then it is very import to make sure you mechanically adjust the steering as close to centered & symmetrical as possible.

- Is the car balanced side to side?
Set the car down on a flat level surface. Use a round tool such as hex driver/thin Philips screwdriver/hobby knive to lift the rear of the car under the centerline of the chassis until both tires are off of the ground. Does the car want to lean to one side or the other?

- Have you checked droop or the down travel of the suspenion?
It seems like when you are turning left the left rear tire might be lifting or not maintaining enough contact with the pavement. Is the left rear suspension traveling down as far as the right rear suspension. If there is a mechanical issue prevent the left rear suspension, this could cause this behavior.

- You cross weight/corner weights look off in your earlier post.
It looks like you don't have enough weight on your Right Front & Left Rear. If you are using adjustable shock collars, I would at least add a thin shock collar spacer to the right front (or adjust the threaded shock collar). This will help prevent the right front suspension collapsing so much during left turns under power.

- Did you measure the springs to see if they are the same length and/or spring weight?
You mentioned swapping shocks, but did you keep the springs on the same corners or move those as well? If you swap the springs from LR to RR and vice versa and the problem follows the spring, there may be an issue with the springs.

I would also check the diffs. Make sure nothing is binding or too loose.