While I don't know the details of your existing converter install, this thread may be of some interest:
Trillium 4500 replacement converter?
As far as an inverter, you need to figure out what you intend to run. I want a 1000W microwave
, so I am shopping for a 1500W inverter. The 12VDC current that feeds the inverter may be as large as 125 to 150 amps. The 12VDC wire between the inverter and the battery
, should be both large, and short. Then just plug into the inverter an extension cord to the load that you want to run. On a set of really good batteries, I would not run a 1000W load more then 45 minutes.