Dear Carla,
Upon further examination and coordination with the Types plugin developer; the simplest way you could attain your suggested layout (from your original screenshot) is to create your own meta box content and just name fields as they were rendered from Types wpcf[$field_name]. We cannot think of any other easier way(as jQuery is even more complicated). Editing HTML structure is not yet supported on Types 1.4 but we look at it in the future release.
You can do this using WordPress hooks like add_meta_box : http://codex.wordpress.org/Function_Reference/add_meta_box then write a callback function that would generated the desired HTML structure. In the form you create, use Types name fields so it will be processed correctly by Types plugin. This requires you have some knowledge in PHP as well. But we cannot think of any other easier way. Please let me know what you think. Thanks.
Cheers,
Emerson