Can't help you with copies, your management should be willing to provide them for you as it would prevent unnecessary write ups. You could also ask someone in maintenance. The references that could prove useful are 737MT 36-006, 737-SL-36-013-B and AMM 36-11-00-710-801 Fig. 502. While the Service letters and maintenance tips are useful, they can't be used to sign off write ups. The AMM or FIM are the references that I would have to use.
Per 737MT 36-006. Normal ops are:
Ground/taxi: WTAI off 18-22, WTAI on 12-14
Takeoff: 37-50
Climb: 37-50
Cruise: 26-45
Idle descent: WTAI off 18-25
The book FCS Explorer is referring to is the Flight Crew Operations Manual, Section 2.20.2 Duct Pressure Transmitters: "Differences between L and R duct pressure indicators are considered normal as long as there is sufficient air for cabin pressurization". Is this all the guidance/info provided to you guys/gals at the pointy end of the plane?
The problem I have with the numbers IFix gave in his first post are that they aren't allowable split numbers, just the tolerance. You could have 35PSI on one side and 33PSI on the other with say 70% N1 and be out of limits.
Per an addition my airline made to our AMM (shortly after the SL came out), we are now allowed a 20PSI split as long as the pressures are between 18PSI and 60PSI. Over 20PSI a 10 day deferral to troubleshoot is applied. Below 18PSI or above 60PSI we MEL or repair the plane.