I love using the cardboard functionality, but there are some things that I think would be nice if they could be added.
First, the ability to teleport without the floor. I understand why this ability is locked to just being able to teleport on top of the model, but maybe with the floor hidden, you could have a floor mesh appear just to teleport to.
Second, an additional mode whereby keeping the button pressed moves you in the direction that you're looking. Obviously, this couldn't replace the current functionality and would have to come with a warning of the possibility of nausea, but it would still be nice to have. There are two different ways of exploring the scene normally, so doing it in VR probably wouldn't be too much of an issue.
These are just some suggestions.