I like all the names on your list except for Cash. Your existing children's names and your shortlist are quite American sounding, I agree. But that style is becoming more and more popular in the UK too. I really like the surnamey style.
I currently teach or have recently taught (in the UK - home counties, 'posh' school) children called:
Aston, Asher, Ayrton, Bailey, Chase, Corran, Enzo, Harrison, Harvey, Hendrix, Hunter, Jasper, Jayden, Jensen, Jude, Lorcan, London, Payce, Quinn, Reed, Rio, Roca, Sandy, Spencer, Sultan, Tate, Tanner, Wilkie, Woody, Zen
Alexa, Atlanta, Aven, Darcey, Dakota, Everly, Riley, Savannah, Sydney
Many of those families are Irish, Scottish or American so I think that surnamey style is probably still more popular in those places but not all are. The girls still seem to be more traditionally named than boys.
Other ideas that I have (mostly) got from American books and TV:
Brandon, Brodie, Cole, Corey, Jordan, Mason, Parker, Porter, Preston
Addison, Ashley, Avery, Aubrey, Blair, Brynn, Cassidy, Fallon, Hadley, Harper, Kendall, Sutton, Payson, Peyton, Piper, Madison, Mackenzie, Morgan, Paige, Brooke, Reagan
Or some other 'softer', 'girlier' options that I think go well with Sutton and Miller:
Amberley, Aria, Aphra, Astrid, Autumn, Alannah, Bronte, Bryony, Bethany, Claire, Cassia, Celeste, Carmen, Carina, Carlotta, Delphi, Darina, Dana, Erin, Eden, Evadne, Ebony, Evelyn, Francesca, Faye, Fenella, Giselle, Giana, Georgia, Halle, Hayley, Honor, India, Iona, Jessamy, Juniper, Kiki, Kirsten, Katrina, Lorelai, Leonie, Leona, Liara, Lena, Meredith, Nicole, Nyah, Nia, Nova, Ondine, Poppy, Posy, Romy, Romilly, Rowena, Rosina, Robyn, Sadie, Sabrina, Serena, Summer, Scarlett, Sienna, Skye, Tiana, Tansy, Tamara, Tamsin, Tanya, Vivianne, Willow
And a few more British (often Celtic) sounding boys names you might like:
Aiden, Aaron, Connor, Callum, Ellis, Elliot, Ethan, Ewan, Fraser, Gabriel, Jamie, Jonty, Joshua, Jake, Kieran, Lucas, Leo, Milo, Micah, Nico, Owen, Patrick, Reuben, Rory, Raphael, Sonny, Victor, Vinnie, Zach