Smkettner has a good suggestion.. in fact when I'm on a questionable power site I turn off the breaker that feeds my Xantrex prosine (inverter) and let it provide power to it's designated clients (TV, Microwave and so on) Now the batteries are charged by a different device so this results in the following line chart
Shore power to---Converter--Batteries--Inverter---Television
I can take shore power that... Well if you displayed it on a 'scope it would scare you, or rather scare me, and it comes out of that prosine as sweet, pure and clear as the best of flutes.. (And I might add I have had the pleasure of listening to some of those, If you do not believe me you need to listen to my daughter, there are better flutists, and I have heard them, but they are not all that many).
But that is an excellent way to deal with the problem
In your case: say a Samalux 300 watt inverter, stand alone, parked near the batteries, and run standard 120 volt wire up to the TV/Electronics bay and put in a couple of additional outlets there.
I suggest using Red or Orange outlets and plates for the inverter powered outlets to distinguish from the non-inverter outlets.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times