I did pretty much the same thing you're looking to do with some slight variations. Here is a schematic of my layout
I went with the Magnum Inverter/Charger, IMO one of the best on the market and made in the USA. I decided to power all the outlets in the coach so I wasn't limited to which outlet I wanted to use. Of course you will not run the AC, but I can run almost anything else including the microwave as long as I use common sense, meaning only use micro for warming or making popcorn. DW can use hairdryer and curling iron and we'll watch a little TV in the evenings. Hence the reason why I wanted all the outlets powered. You still need to practice battery conservation, but it can be done.
I also upgraded my batteries and went with 4 Trojan 6 volts. I keep them charged with a Champion 2000W generator when needed. My plan is to eventually go to solar for charging while boondocking.
I would recommend you add a good battery monitor to your shopping list. I added a Trimetric RV2025. So important that you know how much power you're using and your battery state of charge.
As stated in previous posts you want your inverter as close to the batteries as possible and use the biggest wire possible. I went with 4/0 welders cable from the inverter to the batteries. Made my AC runs with 10/2 Romex w/ground. I ran the romex under the trailer attached with clips screwed to the frame. You can use split loom or flex conduit to protect the wire. Took the wire through the pass through floor, to the back of the trailer and then up through the floor where the load center is located. I bypassed the converter completely. Everything is handled through the Magnum. When on shore power or generator the AC passes through the Magnum and powers the coach as well as charges the batteries. The DC is always hot whether on shore/generator, inverting or no AC at all. If something was to happen to the inverter I can flip the breaker back on for the converter to handle charging needs.
In addition to the links posted previously I would recommend these as good reads also. They are geared towards solar, but contain a lot of information that will help you.
Handy Bob's Blog
Jack & Danielle Mayer