Wow. That is dedication!
You know, playing metal games can be very, very effective with them. It can help them focus on you as the source of their joy, not just the chauffeur who drives them to the park. For mine, one thing we do is just take her milk-bone (she's a freak for milk-bones) break it into little bits, put her in the hall, hide it under a rug in her room, then open the door and tell her to find it. It's a big game and she loves it.
I know others on this site can tell you how they engage their dogs. There are lots of ideas, I'm sure.
I can't tell you why Gigi is nervous around men. It may be something that will just go away with maturity. While I don't think it's a good idea to force her into interacting with strangers, maybe you could enroll in a class (maybe the AKC CGC?) where she is in the same room with strangers, but focused upon you.