Bit reluctant to comment given my own inability to drive a kart fast particularly in the wet but I reckon if you slow down enough to get the kart to change direction, you may as well get out and push it. The thing (without a diff.) will plough straight on as long as the inside rear is loaded. The only other approach is to drive completely off line, and this may well be a very long way round.
So taking TJs badass pic. we can see that he has wound on a lot of lock, we can see he is leaning forward in the seat and we can see the inside rear well unloaded!
I assume that he is at turn in to a fairly tight corner , that he has 'wound on ’ extra caster, moved the front wheels further out from the kingpin and moved the rears in.
As a result compared with a dry setting we have increased the downward movement of the inside front wheel relative to the chassis, and increased the upward movement of the outer wheel.
In effect we are lifting the whole inside of the chassis and driver by forcing the inside front into the track, which is always going to be hard work but can be eased by the driver leaning forward and off the inside rear, but the kart will then change direction. ???