I much prefer
Adelaide to
Ada. That wouldn't matter if you used
Ada as a mn, but as a nn for
Adelaide it just doesn't convince me. I don't think the
Ava issue is important - the explanation is quick and easy, and both names are, let's say, real.
I find Jann ugly and unnecessary;
Jan could work just as well to honour anyone named Jann, and if Jann is a nn (my ex-BIL is married to a
Janet who goes by Jann) then I'd rather honour its owner by using her actual name, whatever it was. I prefer
Adelaide Mary Jann for the rhythm.
Adelaide Claire Annette is lovely. Both mns are good, but I prefer the rhythm of
Claire Annette. That would be my choice.