I actually thought I'd be submitting this without ever knowing what the theme was!
But, finally, having ignored the very helpful hint given by someone earlier, I've got only one left, 5A, but cannot find all six of the "second" words - 16A, 27A, 24A, and 29A all fit, but I can't make 23A, 19A, or 6D quite fit (although 6D is fairly appropriate).