FLT CREW ON ACR MLG ALLOWED CABIN DIFFERENTIAL TO EXCEED MAXIMUM ALLOWED BY TEMPORARY RESTRICTION.

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WHILE FAA INSPECTOR WAS IN THE COCKPIT PERFORMING A LINE CHK; THE FOLLOWING DEVIATION FROM THE TEMPORARY MLG FLT RESTRICTIONS OCCURRED. THIS WAS MY FIRST FLT SINCE THE RESTRICTION WAS ENACTED. DURING OUR PREFLT REVIEW OF THE CABIN DIFFERENTIAL INFO IN THE QUICK REFERENCE HANDBOOK AND MEL AND A DISCUSSION WITH THE OTHER CAPTS WHO HAD BEEN FLYING WITH THE RESTRICTION OF 23000' MAX ALT AND 5 PSI MAX DIFFERENTIAL; I DETERMINED THAT WE WOULD START THE FLT IN THE AUTO PRESSURIZATION MODE SET FOR 22000' CRUISE ALT AND REVIEW THE DIFFERENTIAL FOR AS NEEDED CORRECTIONS DURING CLBOUT. I DID NOT WANT TO PREOCCUPY US WITH A TASK THAT WOULD DIVERT OUR ATTN FROM THE TSTM CLOUD CONDITIONS ALONG OUR DEP; CLB AND ROUTE. WHILE WE DID BECOME PREOCCUPIED WITH THIS WX; INSPECTOR BROUGHT TO OUR ATTN THAT THE CABIN DIFFERENTIAL WAS NOW 7.2 PSI AT 22000'. WE SWITCHED TO STANDBY MODE AND BEGAN EXPERIMENTING WITH CABIN ALTS THAT WOULD ACCOMMODATE THE 5 PSI LIMITATION. APPROX 8000' WAS FOUND TO BE THE APPROPRIATE NUMBER. WE ALSO FURTHER DISCUSSED AND ESTABLISHED A PROC; TO ACCOMMODATE THIS RESTRICTION DURING SUBSEQUENT CLBOUTS AND DSCNTS. INSPECTORS COMMENT WAS THAT MOST OTHER CARRIERS WERE PUBLISHING BOTH AN OPERATIONAL PROC AND A CABIN ALT SETTING. AS A MEMBER OF A 2-M CREW; FLYING IN A DENSE TFC AREA; I FEEL THAT WE SHOULD HAVE BEEN PROVIDED SPECIFIC INSTRUCTIONS TO ACCOMMODATE AN ABNORMAL PROC; RATHER THAN EXPERIMENT OR RESEARCH THE FLT MANUAL GRAPHS MINUTES BEFORE FLT TIME. THE ENTIRE 2-M CONCEPT IS TO NOT BURDEN THE CREW WITH SUCH ABNORMAL DUTIES. MLG ACFT WE WERE FLYING HAD 42944 HRS AIRFRAME AND 55288 CYCLES.