I was just reading this and had a thought
Pebbles can be horrid and when I take her out. Not aggressive with strangers but she pulled on her harness whenever I would take her out with me. I talked to the vet and he suggested a Gentle Leader collar. It really works when I walk her and now I won't go out of the house without it.
The idea is that it goes around the upper part of their mouth (it's not a muzzle and sits far back along the jaw) and then around the back of their head and simulates the submissive response. ****I asked about using one here last week and all responses were positive and other use it as well.
Now when I take her out with me, she sits, doesn't pull and LISTENS to me in public. I realize that listening is not what your issue is but it sounds like there is a loss of control when strangers approach you and she is in protection mode.
This makes you more in control. Also, part of using the Gentle Leader is treats so this is not a punishment and seems to be very effective.
I wonder if you tried this at the dog park and gave treats when strangers came near and she stayed calm and sat, if it would help?