I recorded my qualifying lap:
Turns 4 and 11 were where issues occurred. Fortunately, it looks like my controller problem is effectively limited to only certain cars and tracks. It doesn't actually fix itself, but I evidently don't mash the controller so hard when driving road cars, and it works as usual.
Why do you say that? Is it supposed to be bad for your eyes to sit close to the TV? This is just what works for me - I think it must be because I don't see much but the track ahead when sitting so near.