I prononce it like Brij-it (Bridgit) or Brij-id
Brij-id or Brij-it. I haven't heard it pronounced with the hard 'g' as in Brigg-id.
I am with @gailk - like Bridget with a softer "D" sound at the end. I love the softer appeal of Brigid, but I have never been a Bridget fan and am still not a huge fan of its sound, so I don't think I'd ever go for it, but I adore the nn Bridie! From your options, I like Brigid Mae the best, but I'm not terribly fond of any of them--they're all a bit too short and filler for me. I do like Rae, Mae, and Anne on their own, though.