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I like it. It is very pretty, and I like the meaning. I would have pronounced it like the name Eliza, so I am glad you included the pronunciation! I think Aliza Grace sounds very pretty, but Grace is so common. Since Rose is a family name, I think that would be nice. (I love naming middle names after family members.)
Some other ideas:
Aliza Caroline
Aliza Claire
Aliza Simone