I really like Meredith, and I, too, only like it for a girl. I know a Meredith, and she is 28-years-old. I don't care for Alicia, sorry. I don't think any name is "dated." I like MeredithAlice, and that would honor your family traditions.
I like MeredithAlice too, unfortunately I already have a cousin named Alice and DH and I have a bad association with it from outside the family so I wouldn't use it. Thanks for your input though! :)