I am due with #3, a boy and our last baby. Our older two are [name_m]Oliver[/name_m] [name_m]Bennett[/name_m] and [name_f]Amelia[/name_f] [name_f]Caroline[/name_f]. I like traditional sounding names, but I don’t want to go super popular if I can avoid it. We don’t use nicknames.
My current list includes [name_u]Everett[/name_u], [name_m]Henry[/name_m], and [name_m]Harrison[/name_m]. I am definitely open to suggestions!
[name_m]Hi[/name_m] there.
[name_m]Oliver[/name_m] & [name_f]Amelia[/name_f] are great! I think that [name_m]Harrison[/name_m] is your best bet if you’re not wanting a name that’s too popular. It’s very handsome, & fits in great w/your crew. I love love [name_m]Henry[/name_m], & think that fits in the best. It’s soooo popular though. [name_u]Everett[/name_u] is nice enough. I think a little more trendy than the others.
Here are a few suggestions:
[name_u]August[/name_u]
[name_m]Albert[/name_m]
[name_m]Barnaby[/name_m]
[name_m]David[/name_m]
[name_u]Elliott[/name_u]
[name_m]Edward[/name_m]
[name_m]Edwin[/name_m]
[name_m]Edgar[/name_m]
[name_m]Frederic[/name_m]
[name_m]George[/name_m]
[name_m]Julian[/name_m]
[name_m]Levi[/name_m]
[name_m]Malcolm[/name_m]
[name_m]Nathaniel[/name_m]
[name_u]Owen[/name_u]
[name_m]Peter[/name_m]
[name_m]Philip[/name_m]
[name_m]Simon[/name_m]
[name_m]Thomas[/name_m]
[name_m]Wesley[/name_m]
[name_m]Winston[/name_m]
[name_f]Hope[/name_f] this helps. 
From your list, I do think [name_m]Henry[/name_m] sounds just perfect with [name_m]Oliver[/name_m] & [name_f]Amelia[/name_f].
For a less popular, yet just as traditional name, what about…
[name_m]Philip[/name_m]
[name_m]Edmund[/name_m]
[name_m]Arthur[/name_m] (if you don’t mind repeating the A initial)
[name_m]Louis[/name_m]
[name_u]Laurence[/name_u]
[name_m]Felix[/name_m]
I love your children’s names. My favorite of your options is [name_m]Henry[/name_m]. Some other ideas:
[name_u]Elliott[/name_u]
[name_m]Edmund[/name_m]
[name_m]Theodore[/name_m]
[name_m]Sebastian[/name_m]
[name_m]Virgil[/name_m]
[name_m]Leo[/name_m]
[name_m]Harrison[/name_m] [name_u]Everett[/name_u] would make such a handsome addition to your sibset!!
Other ideas
[name_m]Oliver[/name_m], [name_f]Caroline[/name_f], & ________
[name_m]Caleb[/name_m] [name_m]Miles[/name_m]
[name_m]Wesley[/name_m] [name_m]Nolan[/name_m]
[name_m]Miles[/name_m] [name_m]Wesley[/name_m]
[name_m]Nolan[/name_m] [name_m]Graham[/name_m]
[name_u]Spencer[/name_u] [name_m]Grant[/name_m]
[name_u]Chandler[/name_u] [name_u]Reid[/name_u]
[name_m]Preston[/name_m] [name_m]Asher[/name_m]
[name_u]Micha[/name_u] [name_u]Dean[/name_u]
[name_u]Emmett[/name_u] [name_u]Leland[/name_u]
[name_m]Quentin[/name_m] [name_u]Grady[/name_u]
[name_m]Jonah[/name_m] [name_m]Brooks[/name_m]
[name_m]Maxwell[/name_m] [name_u]Brady[/name_u]
[name_m]Warren[/name_m] [name_u]Elliott[/name_u]
[name_m]Griffin[/name_m] [name_u]Tate[/name_u]
[name_m]Malcom[/name_m] [name_u]Everett[/name_u]
[name_u]Sterling[/name_u] [name_u]Blake[/name_u]
[name_m]Dalton[/name_m] [name_u]Rhys[/name_u]
[name_u]Rory[/name_u] [name_m]Linus[/name_m]
My favourites on your list are [name_u]Everett[/name_u] and [name_m]Harrison[/name_m]. Other suggestions that go nicely with [name_m]Oliver[/name_m] and [name_f]Amelia[/name_f]…
[name_m]Julian[/name_m]
[name_m]Maxwell[/name_m]
[name_m]Reuben[/name_m]
[name_m]Jasper[/name_m]
[name_m]Marcus[/name_m]
[name_m]Gabriel[/name_m]