I like both your names maybe have a couple options for middles names... if your set on the first names then keep them, and just have a couple extra names you can change to suit bub ...I'm with you i do like traditional names - but not overly common... we are going with Jasmyn Isabelle if its a girl and William John Neville if its a boy.... so similar in style to yours.
My friend named her daughter Charlotte Ava-Grace... which i think is really pretty. I think the middle name adds to the first name (plus i don't have a middle name - hence why i love them lol)
As for a nickname for Henry - ppl get nicknames for things they do and like also not just a shortened version of their name.