You can make your own JLofA roster as large or small as you want for whatever reason, have them go where they need to and why. In fact, you can make more than one JLA team.

Couple of rules you'll have to follow on this thread though.

1). The Marvel and DC characters you are only able to use'll have be ones that were born/made in the Earth-616 and Pre-Crisis Earth-One. No other alternate universe characters. Not even characters from alternate timelines (the Days of Future Past one), altered realities (Flashpoint) or pocket universes (Franklin Richards' for example).

2). It can't be with characters who had already died before 1984 which in this scenario will take place. And speaking of which....

3). It will also happen when (in 1984), some Pre-Crisis Earth-1 characters figure out how multiversal and time travel work and made a machine where they can go to Marvel 616's present and past with no issues whatsoever (and won't especially result in alternate timelines being created - which I'm hoping all of you will just go with for this thread).

Other than that, have fun.