G'day JR,
Aircraft pressurisation systems usually have two pressure limits, one that the system should control to automatically and a higher one that the pressure relief valve should blow at.
Exceeding the max diff, with the system controlling the pressure, by a small amount shouldn't harm the aircraft structure. The pressure relief valve is there for when things really go crazy and once blown open will probably stay that way until reset on the ground.
Does your aircraft have a manual mode to control cabin pressure?
Regards,
BH.