Yes it’s legal…There’s no way the police can see my plate when I have my bikerack/trailer-hitch and hauling my pop-up…
Mine is an '03 Ody and the hitch available from U-Haul (or other on-line folks) is strictly bolt-on for the Class II or Class III. It’s an easy 30minute DIY job. I don’t know if the same is available for the '97 but it’s worth a look. The bolt-on hitches are designed to integrate with pre-existing mounting holes in the frame.
The “lighting issue” can be fixed with a harness for external (or trailer) lights. My '03 Ody seemed to be pre-wired so all I had to do was purchase an adapter harness for about $30. Even if that’s not available, wiring a harness into the back vent compartment (inside the trunk, adjacent to driver-side brake light) is a 10 minute job for you or U-haul. If you’re concerned about lights and your carrier obscures anything, you can extend lights, etc. with such a harness. But I agree with MikeInNH that most carriers probably don’t obscure lights enough to be a legal issue. In any event, it’s a state specific question.
Rent a small trailer.
Roof-top carriers or racks greatly increase drag and reduce fuel mileage. The hitch rack is the way to go. Just don’t overload it…Move your license plate if you think it’s a problem…Very few people bother to do this…
I’ll probably move the plate, just to be sure, and try to attach something eyecatching at the back corners. The unexpected extension might catch someone by surprise if they come up from behind.