I think Ava, Joel and Claire work together well. Ava is very popular now whereas all the Joels and Claires I know are adults but I don't think that matters. The sound of the 3 names works.
From your list I also like:
Caleb, Henry, Mason
Iris, Natalie, Eloise
Ava, Caleb and Natalie
Ava, Henry and Iris
Ava, Mason and Eloise
I think you said you're happy with your boy's short list. Other ideas for girls:
Along similar lines to Ava:
Bronte, Bella, Clara, Chloe, Darcey, Daisy, Erin, Esme, Freya, Grace, Holly, Ivy, India, Julia, Katie, Lily, Lucy, Lola, Lacey, Lexi, Lindy, Mila, Macey, Miley, Nancy, Poppy, Phoebe, Ruby, Rosie, Romy, Sadie, Sylvie, Summer, Seren, Thea, Verity, Zara
Along similar lines to Joel/Caleb/Henry/Lucas:
Amy, Anna, Abigail, Alice, Bryony, Beth, Ciara, Carys, Cerys, Celest, Daphne, Emma, Eleanor, Fiona, Florence, Georgina, Hannah, Harriet, Imogen, Isabel, Juliet, Jocelyn, Kate, Kathryn, Lara, Lydia, Madeleine, Matilda, Melissa, Natasha, Olivia, Philippa, Rebecca, Rachel, Ruth, Rose, Sophia, Susannah, Sylvia, Samantha, Tamsin, Victoria, Zoe
Along similar lines to Mason/Holden/Bennett/Reid/Brooks/Nolan
Aubrey, Avery, Addison, Bailey, Blair, Dylan, Dakota, Eden, Emery, Everly, Evelyn, Fallon, Fern, Giselle, Giana, Harley, Hayley, Hadley, Harmony, Jasmine, Juno, Jessamy, Kayla, Kayleigh, Kendall, Kennedy, Livia, Leonie, Larissa, Madison, Mackenzie, Morgan, Piper, Peyton, Payson, Quinn, Riley, Rowan, Robyn, Robina, Rowena, Savannah, Sienna, Saffron, Sorrel, Sabrina, Tegan, Taryn, Taylor, Zia