Sir, 1st of all I will request to forgive me for making this post here as i am not at all a pilot, even never ever seen a plane closer then 2 kms and sorry to still dare to make this reply before so experienced pilots here.
Mr. Minorite invisible asked a problem and I curiously go through all the replies made here but for my disappointment, none answered here the exact solution to the exact problem that been asked. Just in single line of few words he asked that "What is the proper reaction if any?" and none replied to this question.
Anyways, though i am not a pilot still i would like to dare to reply to this question using my common-sense that what could possibly be done to get autocorrected. For this i would like to bring your attention that what pilots do when out of sudden cabin altitude is lost and experience low pressure!!! we immediately needed to descend down till safe cabin pressure altitude or upto Fl100 whichever is safer at it's highest.
Taking the reference of this condition, I think it wil be better to set the pressurization up to the flight level where the cabin altitude and difference get syncronized and then request ATC for descend up to that flight level informing him the situation. Once you recover the cabin pressure normally then again request ATC for your cruising altitude setting the cabin altitude back to the flight level. I think doing this procedure will reset the pressurization system as the system is set to auto instead of manual and you will get the correct difference when you will reach the cruising altitude.
This is not the reply for what been asked but I just tried to put my view using my common sense and once again I am sorry and beg your forgivings for daring to reply among experienced pilots.