Well I tried to follow your "unusual without being too weird" guideline and I hope I succeeded. I found most of these by looking through my old high school yearbooks, but some are the names of family and friends.
Good luck with naming your little one! I love the names are you considering already!

GIRLS:
Amika
Amara
Viviana
Dimitra
Aubriana
Aviana
Eviana
Iriana
Elyssa
Kessa
Tiana
Alanna
Kierke
Camile
Tessa
Chynna
Diera
Chantelle
Sanoe
Rayna
Lina
Larissa
Charissa
Romina
Tia
Sabine
Deanna
Keeley
Fawn
Deira
Stasia
Emalia
Joline
Kira
Elyse
Britten
Ramona
Allandra
Christelle
Rayna
Charlene
Dina
Remy
Ailia
Kaeleen
Maya
Cecily
Cherisse
Meredith
Lia
Seisha
Nyssa
Romy
Felisa
Tiare

BOYS:
Kynan
Kelan
Devan
Myca
Miles
Kendall
Trask
Ryder
Spencer
Cole
Callum
Royce
Garreth
Dathan
Vance
Bryce
Lance
Berkeley
Anton
Tanner
Doran
Beau
Gradon
Kirk
Cutter
Quinn
Oren
Gareth
Gerick
Bronson
Jared
Levi
Troy
Gavin
Dash
Jedd
Chalmers