Just make opting out of each individual question easy (add a N/A or "don't remember" option). Sure, you'll collect less data, but I imagine that you'll get at least partial cancellation after multiplication by the SNR, possibly much more than partial cancellation.
Not all of them, no. Of course not.
But you remember the great ones, and you remember the god damned awful ones. The great leave an emotional mark on you, they inspired you to go into their field, they showed you something that wowed you and has stuck with you over those 10 years. And the damned awful ones leave emotional scars that don't fade, and you'll talk to old veterans/classmates about them like you did a tour of 'Nam together...
Of course some courses lend themselves to imparting this information better than others, and if you end up in fields other than your major there may be less chances to find your learning useful.