The only reason I would use
Elizabeth is because of
Elizabeth Bennett in Pride and Prejudice. I would use the nickname
Lizzie (although in the book it's spelt
Lizzy). I actually really like the name
Lizzie.
Of your list I also like
Beth,
Elsa,
Elisa and
Eliza but I would use the last three as a separate name not a nickname for
Elizabeth.
Other ones:
Lisette,
Lisbeth, Lilibet (this is the
Queen's nickname in the
Royal Family from when she couldn't pronounce
Elizabeth as a young child).