Adelaide and Francis are nice perhaps for middle names. Somehow, I doubt Adelaide though would even be under consideration. I don't like the sound of 'Lady Adelaide.' It's a mouthful, and so spinstery old-fashioned. Addie for short, eh.
Francis or Frances might be considered because of the connection to Diana Frances Spencer.
Oh, I just had a thought that Spencer could be one of a boy's middle names, i.e.,
Philip Spencer Charles or David Spencer Edward or Jonathan Adam Spencer, or John Charles Spencer (in honor of Diana's father and Harry's father). Perhaps Hugh is another possibility, or Philip Mark Spencer.
I personally don't like the name Edmund, but I like the shortened Eddie. As far as girl's names beginning with an 'A,' Abigail seems a possibility in honor of Meghan's friend, with Abby or Gail as a nickname. Maybe Abigail Jeanette Diana (with the middle names honoring Meghan's maternal grandmother and Harry's mother). Doris is also a possibilty as that was Meghan's paternal grandmother's name.
May or Mary are possibilities, as those are names on Meghan's paternal side, and also Mary is a British royal family name. Of course, I doubt very much that 'Thomas' would be considered.