I agree with Kevin as well. I'm running a deep cycle marine battery and wont change my battery configuration until I change my converter. If you dont plan on boondocking alot you wont really know any difference with shore power.
If your lights come on, that portion of the converter works and it should be fine.
...and your right about texas not requiring the brakes under 4000#, but if you go anywhere else you need to comply with that states laws as well, most are 2k, Louisiana is 3 I believe
Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.