Ahh I love Algernon! And Jackson and Carter, too.
It seems you have two options: making a combo of one name you like and one name he likes (preferably with you each pegging the other person's selection as "tolerable"), such as Jackson Earl, or finding a name that fits both styles
I'll suggest some ideas for the second option:
You seem to like well-known modern, trendier names and he seems to like uncommon vintage names with history. So I'll search out some vintage names with a modern-ish sound, with varying popularity.
Silas
Van
Digby
Jasper
Fergus
Audie
Vincent
Otto
Roscoe
Tobias
Montgomery
Ezra
Melvin
Archie (Archer)
Asa
Calvin
Thoreau
Like any? Want more?