Okay, a few more early ones:
Avengers v.1 #14: Tony keeps Steve from falling... by holding his hand.
Avengers v.1 #16: Tony announces that he's leaving the Avengers (for the first time). Steve assures him he'll always have a place with them. One Two Three

These come between #25 and #54, too.

ETA: I realised one of my favourite moments isn't on the list! No!! :)
Tales of Suspense #95: Steve retires as Captain America (a.k.a. the "money" conversation).

And: Avengers v.1 #7: Steve wants to help Iron Man with his problems.

The ToS moment is the latest of all the ones I've posted, I think, and the Avengers #7 is the earliest.