I think [name_f]Gillian[/name_f] is short enough that you might get away with avoiding the nickname, although all the Jillian/Gillian’s I know are known as Jill/Gill (they’re all my parents’ generation, born in the 60s, though so that may not be the same for a baby [name_f]Gillian[/name_f] now).
As for [name_f]Clarissa[/name_f], my instinct would be [name_u]Clarry[/name_u] or [name_f]Clary[/name_f] (as in the Cazalet books).