I attached a link for a good article on inverter installation. I would use method #4 where you wire a 30 amp plug to the inverter output and you wire the inverter output to your converter with an automatic relay. The automatic shut off relay will shut of the converter when the inverter is supplying power.
The article has more detailed instructions and a link to the parts.
http://www.doityourselfrv.com/rv-inverter-install-diy/