I do think Henry will climb the charts sooner or later - I feel like every American TV show has a character named Henry, plus you have celebrities like Henry Cavill and Prince Harry. It also doesn't have spelling variations.
HOWEVER, Henry is such a classic and versatile name that popularity doesn't matter much IMO. It will never be dated, and you have plenty of nicknames to distinguish him from other Henries (Hank, Harry, Hal, Hen). Plus it's a family name for you. Go for it!
at its current rate it will be top 10 in 4 years.
I think its definitely going top 10, which makes me sad. I love it! From your list, I really like Axel. Its unusual without being too different and fits current trends.
I really like Dean. Henry is great too but I'd keep fighting for Dean. Every time I see Dean mentioned in a thread, I think "why isn't that on my list?" Then I remember that with my last name it isn't so great.
My husband has told me that I can name future babies whatever I want too. Sounds like we both have great guys.