I do the "whole house" thing with a GFCI receptacled inverter by plugging the shore power cable into it. The RV's GFCI circuits have no problems at all with that.
Also, I have no clue if the inverter is "floating" or not. Don't care; everything works great. My Honda gen is floating neutral and it works great too.
Only issue with all that seems to be if you have one of those Ewhatsit gismos that I don't have, when you have to use a bonded plug adapter. Easy solution is don't get one of those gismos! I do have a surge protector on the shore power cord, but that is a different animal.
