Ahhhh... so the front wheels DO have a little toe-in. I was wondering if it was intentional or if the rack the turning front wheels were on was just not made too well. Also, I found an interesting solution that has reduced the problem somewhat. The front wheels have some freeplay in the vertical axis, sort of similar to the BCGs. The front turning axle is actually mounted on a sort of bump on the chassis creating a rocker and while there's no real suspension of any sort, allowing the axle to rock lets it deal with ground that's slightly uneven i.e. carpet.
However, the caster combined with the toe-in, (toe-out as you pointed out in reverse

) and the instability of the rocker axle makes the car extremely unstable going backwards and therefore, the turning in all sorts of unwanted directions in reverse.
My solution was to first reduce the amount of travel and freeplay in the vertical axis so I just rigged a 'damper' of sorts using folded card which prevents the wheels and axis from wiggling up and down as much and voila! Instant improvement. The car now has some semblance of control in reverse. Problem is that the reduction in wheel travel and the ability to cope with uneven ground, has also affected the cornering ability and stability of the car going forward at maximum speed. i.e. when I set the speed and acceleration on the Propo Special to maximum it tends to traction roll in turns a little more.
SO... now for modifications part II, by dissecting a Bit clone, I'm going to try and adapt the centering spring for the Bit's front axle to the Digi Q's turning front wheels. I think given how small the spring is and how weak, it shouldn't interfere with the wheels' ability to turn when it's supposed to, but it should hopefully be enough to keep them pointing straight when no steering input is made, in other words when no lateral force is applied to the front wheels.
Hopefully this works, it would also solve the problem some other people have noticed about playing with the Type-R cars with turning front wheels on small area surfaces such as table and desktops. After you stop, the car tends to start off in the direction its wheels were last pointing when you stopped. Which in some cases leads to the car jumping off a cliff
Well, if anyone's interested, I'll post the results of my attempt to do this mod.