My only thought so far is 'bea' as a middle name, but the name we want as a first is also one syllable, and so is our last name. Is that too much?
Beatrice maybe? It has the 'Bea' beginning, and a 't' too.
I would avoid a single-syllable first name. I have a single syllable last name too, ugh. Short/single syllable firsts just sound choppy and - short. Most of the time, she would be called by her first and last name...
Perhaps Elizabeth Ever or Everly Elizabeth? Bettie would be a diminutive of Elizabeth, and Ever/Everly are taken from Beverly.
Beatrice is a perfect suggestion!
Difficult one! Beverley and Bettie I honestly don't know how you would combine them to make a new name...!
Beatrice - has the length of Beverley and includes the 't' of Bettie
Bethany - has similar start of 'Bev' 'Beth' including similar ending of Bettie
Bevie - has the nickname quality of Bettie and is a variant of Beverley
Babette - has the length of Beverley and has the 'ett' sound of Bettie.
Bea - as obviously both names start with 'b' sorry running out of ideas
You could use names beginning with B:
Or you could use variants of the names to make a new combination. For example 'Bettie' is a nickname variant of Elizabeth. Obviously Beverley is a name in her own right. But the name is closely linked to the more modern Waverley as they have a similar sound. Due to this you could combine both Elizabeth and Waverley to make a very pretty more up to date combination that links to your Grandma's. I like the idea of Elizabeth Waverley!!
Anyway hope this was of some help.