40 odd years of history with the big seven only being a creation of the last 10 years or so, I find it funny that you think its not the JLA without them!
Firstly the big 7 that came about with Morrison is pure bullshit. Wally and Kyle were not the "big" GL and Flash, thats Barry and Hal, whether you like em or not. J'onn was a member for 5 minutes in the 60s, and didnt return til the late 80s.
I don't know about "big seven," but there's definitely a "big six" and has been since the sixties.
From 1960 to about 1984 (24 years), the core JLA was almost always: Superman, Batman, Wonder Woman, Flash, Green Lantern and Aquaman. They weren't in every issue but in any given issue the majority of them were there.
There was a brief period in which WW lost her powers and wasn't there, but during that time period everyone felt like she was because of the SuperFriends show, guest appearances by the GA WW, guest appearances by the depowered Diana Prince, etc.
From 1997 to the present (10 years) the majority of the stories featured these six. Maybe not always the same Flash, or the same Green Lantern, but heroes with the same basic powers and the same name.
So, for 34 of the 47 years there has been a Justice League, you've had a more or less consistent roster of these six plus various other heroes.
That says to me there is definitely a "big six," if not a big seven.