It's so funny that
Minna seems quite exotic a name to anglophones. Here in Finland it's a very common name (especially among females born in the 1960's and 1970's) and that way plain to me.
That said, I definitely prefer
Minna to
Minnie.
Minnie is too nickname-y, but it works as a pet's name and, yes, as a nickname (e.g.
Minerva "
Minnie" would be cute). I know that
Minna is also ultimately a diminutive of
Wilhelmina, but it would still work as its own. Of your combos,
Minna Florence,
Minna Constance,
Minna Lucille and
Minna Dorothy are prettiest to me.