I'd suggest to buy an extension cord long enough to reach the entertainment area and either hardwire a box with
this type of receptacle or equip the box with it's own male cord set end. Some depends on the permanence of your situation regarding the inverted power. In lieu of an extension cord, you can just pull 12 ga. or 14 ga. residential wire from the inverter to the location where you need power.
You could buy and install an additional 15 amp transfer switch to enable inverted power to all your receptacles or, like Pianotuna mentions, plug your shore power cord with adaptor into the inverter. The case against that is that it is that 300W of inverted power is not going to power a lot of 120V devices.