coming from a [name]Jillian[/name], trust me, use a J! my brother calls me gills with a hard g just as a nn but I thank god everyday that my name starts with a J!
[name]Jillian[/name] One of my best friends is [name]Jilian[/name] (with only l) i think that way is gorgeous…But definitely [name]Jillian[/name] or [name]Jilian[/name]
My little sister’s name is [name]Gillian[/name], pronounced with the hard g sound. EVERYONE outside of our family (and sometimes even they slip up) says it like [name]Jillian[/name]. We usually call her [name]Gilly[/name] so people know how the G sounds.
If you want the soft g sound, go with [name]Jillian[/name]. I don’t think it looks made up, personally.
My name is [name]Gillian[/name] pronounced like gills on a fish, and I can tell you from experience that getting called [name]Jillian[/name] is a common, everyday occurence for me and ALWAYS has been. Everyone always tells me it’s a pretty name and I love the uniqueness of it now that I’m older, but as a child I disliked my name. However, I do prefer my name to [name]Jillian[/name] 
[name]Jillian[/name] seems more natural to be and looks nicer to me, I don’t think of it as a made up spelling even if it’s not the orginal. If you prefer [name]Gillian[/name] go with that, pronouction problems won’t be that bad, but really [name]Jillian[/name] is fine.