A 300WATT INVERTER is NOT going to be large enough to do anything but perhaps drive your Home Entertainment items and some Computer and Cell phone chargers etc... It is alot of effort to pair out the 120VAC Circuit to either run off of Shore power or Emergency Power or Inverters... I would be thinking if it was large 3000WATT Inverter setup it would be worth the effort.
INVERTERS are also very BATTERY DEPENDENT. They consume alot of battery power when being used. Check your install manual for how 12VDC current it will draw when being used at full power. Probably around 25 AMPS... This may require a min of 255AHs Battery Capacity to make it through ONE night. This is almost the amount of DC CURRENT we draw from our batteries with our 600WATT Inverter for some 120VAC items and some Battery direct connected for all the thing we want to use in ONE night in our off-road camping. This drops my 255AH Capacity Battery bank down to 12.0VDC over nite which is right at 50% power. I never allow the battery bank to below this number so that I won't do damage to my batteries before the get re-charge as soon as possible.
If it was me I would just plug in a coupe of multi-head 120VAC Extension Cords and run one to the Home Entertainment area and the other to the night stand next to your bed.

I also don't think the GO POWER INVERTER you have is a PURE SINE WAVE model which means you may have to watch real close what you plug into it. The consensus is anything ELECTRONIC requires a PURE SINE WAVE type Inverter to be 100% safe. Electronic items like to go up in BLUE SMOKE the instant you plug them in. Anything that uses a Electronic Module controller is definitely prone to damage. The best approach is just always use a PURE SINE WAVE model Inverter and never worry what anyone else will plug into them... The Early PSW INVERTER were alot more expensive but that not so much true anymore. My DUTY 600WATT INVERTER is a PSW Model and only cost $149 from AMAZON.
I am still using my original three GP24 12VDc Interstate 85AH Batteries installed in 2008. I originally had 4ea Interstate batteries but boiled out battery fluids on one which shorted internally before I realized I needed a smart mode charging system
Just my thoughts here based on camping off the power grid alot for the past five years or so... I'm sure others will tell you differently... Everyone has their unique experiences on what works for them.
Roy Ken