I think you've hit the nail on the head. Your two major points are those which I hope DC is aware of and needs to heed in setting up a new series.
1) The JSA ain't like other teams. Their historic placement and their age are points that either make them special and worthy of being kept around, or problematic and disposable (which some at DC believe).
2) The JSA needs fans of new blood. I still maintain that the JSA fanbase, although loyal to a fault, are older and actuarially speaking, a decreasing cohort. Sure there are some, but in order to get more than just us (and we know who we are), more are needed to provide at least some sort of cushion saleswise. Would a Roy Thomas "fit it all in and reference old books" approach work for current reading proclivities? I recognize there is a challenge there and it would take a fan (or at least a historian) to make a team book with yet another Flash and Green Lantern stand out.
And then sometimes, I just wanna stamp my feet and scream "I want it!"