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I've encountered Eckie as a Scottish nn for Alexander, so Eck seems OK.
I've met an Ant. I think he was Anton rather than Anthony; close enough.
The -z instead of -r is standard in the UK. I know a Derek, nn Dez, and there are lots of Sharon people known as Shaz; also Karen = Kaz. So Gaz and Jez (why the extra z?) and even Muzza are fine. There's also an -r to -l possibility: all I can think of now is Terence or Terry becoming Tel.
Joani is just plain silly. A spelling variant cooked up by those who think Joanie is too old-fashioned ...
Tori or Tory or Torie are standard shortenings for Victoria, likewise Vicki, Vickie and Vicky. So I don't find it necessary to make Tor and Vick separate entities.