I also don't think Iris is too popular. Even for names that rank top 100, it's only the top 5-10 that you literally hear everywhere and have multiples of in a school year group. Below that they're just well recognised names. I love Iris.
Cora - quite like it but prefer Cara
Willa - not keen. I do quite like Willow though I'd worry about the child not being willowy looking and getting teased (ridiculous, probably!)
Alma - not keen, I agree with your assessment. I do really like Alba though.
Nina - sweet, I like it. All the Ninas I know are Indian but that might just be coincidence.
Rosa - I like it but prefer Rose, Rosie and Rosanna
Camille - not keen but I do like Camilla
Other ideas you might like:
Aphra, Ada, Asha, Bronte, Belle, Carys, Carrie, Etta, Esme, Effie, Eliza, Elora, Fern, Faye, Giselle, Greta, Honor, Hope, Ida, Iona, June, Joy, Josie, Kate, Lorna, Laura, Liara, Marta, Mala, Mila, Mina, Mira, Meryl, Mirren, Meredith, Noa, Nora, Orla, Opal, Robyn, Romy, Remy, Rowan, Rita, Seren, Sorrel, Sadie, Susie, Sylvia, Thea, Taryn, Tegan, Tamara, Una, Verity, Vita, Winona, Yvette, Yolanda, Zillah, Zeryn, Zelda