I hatee
Bill,
Billy,
Billie .. I'm not even sure why.
I love
Liam, even as a name on its own.
Will is great, and it ages well.
You don't alwyas have to have a nickname, but since you said your other kids have short names that might work out ..
Try things like this:
William Oliver .. W+Ol .. Wol
Just other random thoughts, I'm not sure what you're into as far as names.
Wollie
Wolly
Wilv
Wiver