I know some people use a rope halter but I hate them. I use a regular halter, if I need a little more control I run the line over the poll. I don't have a cavesson because I am poor lol. I agree that it's a training thing. He is used to having physical boundaries, now he just needs to learn that the line is the boundary. Just bump him off of your hand and he'll figure it out.
I have seen horses lean just because they're unbalanced, though if he is fine in the roundpen I think it's just a "boundary" think.