Welcome to BPO, and may I say Persephone is beautiful!
I have to jump on the prong collar bandwagon here. When used correctly they are a wonderful training tool, think power steering for your dane.
I have three dogs, and all of them use one. Raven is a bolter, she would be gone in a heartbeat. The prong reminds her that she is not the one in control. Strider is an idiot. He is a puller, and would break his own neck with a slip collar, or kill me with a harness. He also has the attention span of a gnat and likes to chase anything that moves. The prong keeps his attention on me, rather than the dog down the street or the squirrel in the tree. Merlin is the best (and largest) of the three. My 90 lb daughter can walk him with a prong collar and a peice of dental floss no matter what the distractions around him. In his case the prong simply exists on his neck as an insurance policy, it is rarely if ever needed. Keep in mind, once you have her under control and responding to you alone, you can switch her to a less severe-looking collar.
I would also say try group obedience classes as well. Desensitize her to the distractions by putting her in the middle of them for training.
Stella