The 737G cannot be certified beyond 180 minutes. You need to have the APU running between your ETOPS entry and exit points unless your on a special approval for an APU maintenance program in which case you do not need it to be running. As other have said there is a lot more to this than what is obvious. The fire suppression is the limiting factor.
Many airlines fly the NG between the west coast of the US and PHNL which requires 180' authority.