Wes,
I have to give this one a big ,"Hmmmmmm...". Isthe Inverter output isolated
from (chassis) ground ?  If so the GFI is useless since there is not a
current path through the body of the car back to the inverter. Logically,
the inverter chassis would be at DC  ground potential and isolated from the
AC output. AT least, that's the way I would design it. That way you couldn't
get shocked standing wet and barefooted in your van making margaritas.
Ken Lewis
http://neksiwel.20m.com/
in statu viae