There should be a ground lug in the AC load distribution panel that you could connect to (do not disconnect what is there, connect in parallel) and this will make the AC load panel ground "common" with the AC load panel. Also, if you connect your trailer to outside power or to an external generator, the inverter will be shared ground with them as well.
A word of caution.....EG4-6000XP output 240vac on L1 & L2 with a neutral. Be sure you do not back feed the EG4 if you power your trailer from an outside source. It is not self isolating on its output.