When I first read Suza, I thought like the tequila? But then I remembered that the tequila is Sauza. I like the suggestion of Susannah with the nickname of Suza.
I think shortening a common name as a given name is ok...personally I would prefer that my child has the longer name and they can then choose to go by the shortened version if they want, because I like the history behind names. But especially in the case of a made-up name, if it has special significant to you and your husband, then go ahead! Made-up or mash-up names can be quite noteworthy...just think of Quvenzhané Wallis! (her name is a mash-up of both of her parents' names, plus the Swahili word for fairy, if I'm not mistaken).
I would totally go with the more formal name of Susan (or Susanna) and call her Suza as a nickname. People will assume Suza is a nn and she is bound to be asked about it a lot. I can't help but think having a more formal name to fall back on would be appreciated. I happen to really love the names Susan and Susanna(h). From your list of other considerations, I like Petra.
If I met a kid named Suza, I would assume her parents were big into marching bands. I think that you and your husband are so far apart stylistically, that you're going to have to come up with a compromise. I think your best option, as others have said, is to come up with a traditional name that satisfies him with a quirky nn that you like.
Susan/Susannah- nn Sosie, Zanna, Zuzu
Beatrice/Beatrix- nn Trixie, Betsy, Bixie
Elizabeth- nn Libby, Zibby
Catherine- nn Kit