Will we ever find a name we agree on

Well your DH has more contemporary taste and yours is a bit more traditional op. So you’ll need to meet in the middle I guess.

How about:
Camille
Paloma
Lyra
Eloise
Sylvie
Mia
Leah
Seren
Estella
Layla
Lara
Clara
Chloe
Lois
Marnie
Maisie

Of his names I think Cleo is the best.

I really like a couple of names from both of your lists - I think there are definitely names that overlap both of your styles. DH and I had a similar problem, we went through the ons names list together and wrote down any names that we liked - didn't have to love - then compared lists and there were about 5 names that featured on both lists so that was our shortlist, as it happens we went for one on your DHs list!

How about
Emilia
Mila
Ada
Freya
Joss (nn for Jocelyn)
Clara
Winnie (nn for Winifred)
Mabel
Beatrice
Grace
Leila
Penelope/Penny
Noa

What about Juno?

So a long winded but fun (for us) game my DH and I played when we were in the same boat.

1. Each prep a list of names you like (we went with 1 for each letter of the alphabet). You need an equal number of names.
2. Write each name on individual scraps of paper, so you each have a pile in front of you.
3. Choose one name from each of your piles at random to put side by side.
4. Discuss the names, choose one winner from the two. Put the winner into one pile and discard the other.
5. Continue for the whole pile of names.
6. You should now have a pile of 'winning names' and a discard pile.
7. The next stage is to bring out two names from the winners pile each time to compare, but this time it's winner stays on.
8. So say you bring out Mary and Cassandra, and agree Cassandra wins, Mary joins the discard pile and you draw another name, so now you have Cassandra Vs Alice, this time Alice wins....and so on until you've gone through all the names and hopefully have found a winner.

We did it over a long dinner, and it's actually how we chose the first/middle name combo as two names came out together which flowed nicely.

It makes an event out of it, you get to sit and connect and joke and debate, and hopefully come out of it with a name you both agree on.

Chloe
Jasmine - Jazzy
Daisy
Scarlett
Indigo
Flora
Cosima
Cosette

Would you do a Susannah, nicknamed Suki?

Both you and DH have largely followed your personal existing patterns (you with the EE sounding ending, him with the C names, aside from Indie). I would suggest you both come up with some options that break away from your existing patterns, otherwise it does just feel like you are naming another child with your respective exes, which understandably won't go down well with each other.

You like traditional, whilst he likes more unusual names. Could you find a traditional, with a shorter nn?

EG.
Jessica, nn Jess
Kimberly nn Kim
Indiana , nn Indie
Lucinda, nn Lucy, Cindy

Suggestions
Emilia
Hayley
Eliza
Tilly
Zoe

I would avoid a C name, otherwise you are following the pattern set by his DC and your three are left out.

What about Camille? More classic like your list but a bit more unusual like his list and begins with a C.

Charlotte.

I like Cassie but it's too close to Caspian.

Cecily

I dont think the lists are that different.

Yours are more everyday, but they are all short and feminine sounding. Yours all end with an ie sound 2 of his do too.

Im sure you can hit on something.

I personally like cleo and suki best.

I don't think he should really choose Cassia if he has a Caspian.

I think Clara is a good suggestion.

Cassandra, nn Cassie?

FWIW I think your dc selection would actually benefit from a non "ie" ending to provide a bit of aural contrast.

ETA he seems to like names starting with C. Could you start there?

What about Callie?

I like Indie , I think it goes well with your 3 children’s names @Tomsthetriumph

Use one one those baby naming apps where you both rate names independently and see if there are any you are both ok with .
Your tastes are completely different but that way you may be able to find something that you can both live with. I don't think you will find something you both love.

Astrid
Allegra
Evangeline
Jolie

You do have very opposite tastes! (I like yours although Cleo is nice).
Maybe scrap both lists and both try to come up with two names in the other person’s taste.
For example you like quite classic names so he may suggest Florence or Annabelle.
I’m not sure how to describe his taste but you might put something like Fae or Bea.

Think each other’s tastes but something that you like.

Very different styles but you are not the first couple with this issue. His name list is a lot more individual whereas yours is more main stream. I think you need to list names and score every name 1-10 or 1-5 and then work on the top ten list as that is the compromise area.

Do you like the names because of how they sound or their meanings? For example, is there a spice that is more common than Cassia that you would like? Instead of Suki and Ruby go for Suzy? Name Clarissa but call Cassia?

I love your list beautiful names your husbands sound like cars

How about

chloe
cora
romy
sadie
pippa
daphne
pippa
clara
thea
callie
iris
jasmine
rosa

Some in the middle names that might be vintage but modern: Mabel, Cora, Sadie, Emmeline, Petra, Bryony, Clementine, Juno, Juniper, Hallie, Callie

Cassia is an odd choice seeing as he already has a Caspian! For what it's worth I much prefer your names. However, maybe you each need to list 10-15 more names to see if there's any common ground. Feels like there's going to need to be a compromise somewhere!

Clara
Isla
Ingrid
Elodie
Romilly
Rosie
Suzy
Suzette

Just a few thoughts, tyring to combine styles though I'm probably leaning more towards your style.

(Is China a boy or a girl? Do you know the reason behind that name?)