This may be a wacky idea, but just thinking out of the box.
You have a rear parking brake on it, right? Not a transmission brake?
If so, wonder what happens if you engage only your parking brake while driving? Taking the front brakes out of the equation, would it still dart to the left?
Just an idea.....

~ Victor
1941 3/4-Ton Pickup (in process). Read about it in the DITY Gallery
1955 Grumman Kurbside "Doughboy" 235/3 on tree w/ OD
1957 3100 - moved on
1959 C4500 Short Bus "Magic Bus" - moved on
1959 G3800 1 Ton Dually "Chief" - moved on
1958 C4400 Viking "Thor" ~ moved on to fellow Bolter