Derfred says that my suggestion of telling the "Computer" that the Cruise Level is 1000' above actual will not work (in giving a buffer) in the 737NG. If that is so, why bother telling the "Computer" anything about Cruise Level? Interesting to note the comment on scans. Seems to be very much a reliance on the aircraft monitoring itself. I just hope they are close to infallible.
I think the problem is that none here really knows the wiring inside the pressure controller. I speculated that the opposite might work, i.e. setting a lower cruise level in the window of the CPC. More specifically setting it to a level where the max diff pressure is 7,80 instead of 8,35. The aim being to somehow 'trick' the CPC so it increases cabin altitude until 7,80 is achieved.
Hand on heart it's happened more than once to me that we've flown the entire sector with the pressure controller set to a different cruise level than we've actually flown. That is not say that we're not monitoring the actual cabin altitude, vertical speed and differential pressure at regular intervalls.
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.
There is no direct checklist for the situation as described initially. The system should've activated the AUTO FAIL light and either the second CPC should've taken over or manual control of the cabin pressure should've ensued. It didn't happen. Discussion about the CPC with the information we've got in the FCOM/AMM has taken place. It's been a useful thread so far.