Errr ..... hang on......
"....The inside wheel and the outside have different effective gear ratios while cornering...."
No they don't! They both have IDENTICAL ratios ....... BECAUSE we have a solid axle. There can NEVER be a circumstance when the two rear wheels rotate at different speeds.... EVER!
I don't actually believe you meant that. Do you mean that, like runners on a track, the inner wheel travels a shorter distance than the outside wheel? That's agreed; however, the effect is ALWAYS that the outside wheel retains traction and the inner one rotates FASTER then the track moves past it. That's akin to applying too much power and letting the wheel 'spin' which is a good way of accelerating. However, surely, that HAS been occurring since the moment the kart started to corner, at that was at the initial turn-in. If it hadn't, you'd simply have gone 'straight on' until you hit the barriers.
If I've misunderstood you, please explain with more detail of what you are describing.
Ian
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