Adding a small inverter

Isn't the converter behind the fuse/breaker panel? It is in my 180. You can tap 12V there and then feed the TV breaker from the inverter. Maybe run 12" of wire?

Don't mess with the breaker panel. If you want to put in a permanently installed inverter then put in a receptacle for it. Use a different colored receptacle and face plate so you don't get them mixed up. A 300 watt inverter will require about 30 amps at 12V so you would need to run a minimum of 10 awg wire to it. And be sure that there is a 30A fuse on your new 12V line to protect that wire. 

Not sure where everything is located in the 189. I tapped the supply for the stereo for my 12V port because its within a foot of the TV. That is already on a 10-15A fuse IIRC, so the port and wire is protected but would not support full output from a 300 watt inverter, more like 100 watts max. I have a 300 watt inverter I've used a couple of times in my port but just to charge a laptop, much less than 300 watts. The TV uses much less than 300 watts as well so its wouldn't be a problem, but if you want to use more power from the inverter then you'll either need to tap a circuit with a bigger fuse or add a new circuit and fuse.

I saw a comment that it is rated for 120W which would be 10A. That should be fine for the TV. If it is 120W rated then put it on a 10A fuse and call it good, don't try to feed it more current than its rated for. The only drawback I see is the LED parasitic loss. Unfortunately you seem to rarely find one of these without the LED anymore, mine has one too. Its a tiny load but you would still want to disconnect the battery or leave it on charge while in storage. 

If you are digging around in the cabinet with the converter, you can tap into the 10ga line that feeds the 12vdc heating element of the fridge. On mine this wire bypasses the converter, is orange, and is fed thru a self-resetting circuit breaker mounted to the floor inside the cabinet.