I wondered whether I could put multiple layers of a horizontal grid over the tomatoes instead of cages. This would be less obvious than a cage, and allow easier picking to boot. Then last Summer I saw an episode of Bryce Lane's In the Garden where he went to the home of fellow NCSU hort professor Will Hooker. Hooker was successfully using horizontal support for his tomatoes, so I decided to give it a try. Here's a picture of in from June 15. I used nylon mesh with 6" openings. There are four layers, each about a foot apart:
As of June 29 the tomatoes are all the way through the top layer and I have picked my first ripe ones of the season (the wonderfully reliable Juliet, a grape variety):