I have a EU300I on the tongue of my camper. It actually halps offset the weight of the motorcycle that I usually carry on the back.
I cover the genny with a gas grille cover when I am on the road. I have a big 5/8" cable and HD padlock through the genny handles and tongue for security. I strap mine down with cargo straps. It is nor a permanent installation because I need to remove it if I don't carry the bike. Otherwise my tongue weight would be too high. I also remove it when I put the camper in a storage lot. Too many envious eyes.
Note that as smooth as the Honda runs, it does send some vibration through the frame. You might want to run a test before you commit to a final installation, as the vibration may be objectionable to you.