This is not a full answer
It is too much for a comment
Please don't vote this down
But don't vote this up either
As for tire size that is not the problem.
My theory is you need to correct but I cannot demonstrate how much.
A larger tire is good as you will get the same amount of traction for less force.
Bike geometry is designed to hold a line on a flat cant.
If you hold a bike by the seat and balance it on flat ground the front wheel will be straight.
If you tilt the seat to one side or the other the front wheel will turn.
This is how you can ride with no hands.
So if you change the slope under the bike it is going to affect the natural line also.
I ran a test where I tilted board under the bike compared to tilting the bike on the board.
What I found was the wheel consistently pointed down hill - which made sense.
I think this needs a free state diagram that mechanical engineers do and I don't know how to do those.
Hopefully a frame designer will get on.