I love Cornelia - said as both cor-neel-ee-uh and cor-nell-ee-uh! It’s clunky and grand and lovely and it stands out in a good way imo! You’ve got very usable nicknames and for me, it works just fine with Lucy, Evangeline, and Susanna at least.
Cora is sweet but sharp and I can see it would fit better with Ruby, Ada, etc but reading your words, Cornelia still seems to be the one speaking to you - and the fact not having it on your list hurts your head is a good sign to me that it should stay 
(as a side note, if you went with Cora, Cora Jubilee, Cora Beloved, Cora Sunshine, Cora Winsome give me a similar vibe to Cora Blessing or Cora Joy?)
A few potentially less helpful points:
- as someone else who’s just collecting, I’d just keep both and switch it up every now and then to which was speaking as my fave that day
- if you want them to lean more real-world usable, would it help to have Cora as a first name in a combo and Cornelia as a middle for something more grounded/familiar/more universally liked? Like Josie Cornelia, Joy Cornelia?, Hazel Cornelia etc, so you get to have both on your list?
- Ugliness/beauty in names is so, so subjective - and this is for your list, not anyone else’s. If losing Cornelia feels too wrong, I’d keep Cornelia. But if it feels too uncomfortable to have Cornelia on your list as a first name, maybe Cora is the better option
All that big ramble to say, my personal preference is Cornelia and I’d go with that 