Yes, try out different stuff to find out how it really works. But be careful to compare apples to apples.
The energy needed to get a tire spinning, or change the amount it is spinning, is its moment of inertia ("I").
The moment of inertia is the mass ("m") times the square of perpendicular distance to the rotation axis ("r"): I = mr^2.
Now what does that really mean? Well, that "mass" is at a point somewhere out from the center of the axle ("r"). You can get "m" by weighing the tire... but the wheel contributes too so you should weigh it too... trouble is, the tire's weight matters more than the wheel's weight because it is further away from the centerline of the axle.
For a tire mounted on a wheel, which in turn is mounted on an axle, "r" can be measured from the centerline of the axle to anywhere along the sidewall of the tire. You'll get different answers depending on where along the sidewall you choose to measure - especially because this measurement needs to be squared in the calculation.
Your stock car's tires are a lot bigger in radius than a kart's tires. The kart probably has a better power-to-weight ratio than the stock car. So while you can do these experiments to get a general feel for reactions to different size tires, the two vehicle's size and power differences can skew the overall results enough to fool you if you're not careful.
Then you have the question of "what are you trying to optimize?". Acceleration? Corner grip? Drag? These can work against each other.
BTW, for the question of where to measure "r" on the tire, I prefer to use the outer (tread) edge of the tire. Since the "I" calculation is sensitive to this "r" value, I use what I feel is the "worst case" which would be the longest possible "r". If the track tends to stay heavy during feature races, I measure "r" on a tire after I come off the track and the tire is still dirty (I include the thickness of the mud). For "m" I also weigh the wheel / tire / mud assembly. That buildup of mud is heavy enough to effect the calculation - especially on small tires like on a kart. I weigh while the mud is still wet because it will weigh less when it dries.
Now what do I do with the results? Compare them to what the stopwatch says.
In my experience with both stock cars and karts, I've found that often the stock car has more horsepower than I can hook up to the track while the kart is opposite (it is too easy to bog the kart motor down by getting the tires too hooked to the track). So for stock cars it was more important to optimize tire grip for turning... for karts it is important to balance tire grip with engine torque.
I'm not faulting your idea, I'm just trying to warn you about my own problems while travelling down that road.
