I have one of those 7 port charging docks, but yes the inverter must be on. This is an obvious downside for dry campers.
I tried a multi outlet USB thingy plugged into the power port on the dash (it is always on in our E450 motorhome) and blew the fuse. oops. Works fine to charge 2 iphones though.
Best solution for sure would be to install a few of those wall mounted USB ports posted above in strategic locations in the RV (bonus points for the little net idea, I like that!). It's on my 'to do' list, but until then we're just running the inverter 24/7 and taking the power hit.
