If you are only using the inverter to run a Television then maybe it would be easier and, possible even cheaper, for you to get a newer Television. A lot of the new ones draw so low of a currant that they have one of those little black boxes where they plug into the wall. After that they use a small wire to go to the TV. The black box plugged into the wall is actually a power inverter and the TV is running on 12 volts. 
Then you buy , or make , a adapter and run he TV off of 12 volts directly from the battery. Therefore bypassing the invertor you are suing now. 
There has been a lot of talk about this over in the "General RVing Issues section. Do a search or ask members about it. I'm seriously considering doing it myself this year.