Tyres seem to be a very much outdated design offering less than optimal lateral grip and stability
There's just about nothing between the thread blocks to keep them stable and the pattern will make them follow ridges in the road .
I'd think you may be better off with something like this
Reifenwerk Heidenau
What size are they ?
8" by 4" wide (size I got from the googling mitas super B5) ?
If so, that seems to be limiting the choice a lot .
Dual compound scooter or motorcycle tyres could offer a lot of grip on their sides.
Front compound is softer as it doesn't have to lay down power, but the harder part of the rear tyre is narrower - so you'd need to take into account the camber to see if you'd really be running on the softest compound of the front tyres.
Cool video
That 3 wheeler was passing you in the hairpins where I'd think you could go faster
Three-wheeler seems to have bigger wheels, is that right ?
But your kart is faster
With a shell, it'll go faster still (aero + a bit extra weight) so it needs to turn better as well.
The driver is laying down - so it's very low.
That kind of design won't work with your upright seating position
You'd still stick out like a sore thumb
ChazinMT's design is more suited for what you've got, but enclose the rear wheels as well ; and make the headrest fairing narrower or round off the front some more.