Later you climb to 37000' [as per the new clearance]. But still 27000' is set as Flight altitude.
Mistake number 1 obviously,check SOP and/or make sure you are awake,if unfit to fly,call in sick.
1. Will cabin altitude increase to maintain 7.45 psid ? or
2. Will differential pressure increase to maintain 4500' Cabin altitude?
The system will overpressurize the cabin. When the differential pressure limit is reached, the system will first try to relieve pressure by opening the outflow valve. Under these conditions the pressurization system will allow the normal cabin rate limitations to be exceeded which will result in high cabin rates. Depending on the magnitude of the difference between the selected and actual FLT ALT, the pressure relief valves may be activated.
Boeing system is based on competent pilots being seated at the pointing end.
However mistakes happen due to unexpected change of levels,distractions...so the highest achievable flight level for your flight should be set before take off.
This level can be determined from you flight plan or if your ATOW is lower than expected by checking in the FCOM,under max/opt flight level based on weight,OAT and bank limit.
If you never reach the set level,it should be reset before top of descent or during descent checklist,in case it is not done,the worse that could happen is an offschedule descent caution,far fetter than operation of the pressure relief valves.