I believe I have found where it fits in regards to JSA.
Sin Corps Special shows the JLA fighting Zoom in Keystone City, but he escapes. Sinestro War starts.
JSA #8 we see the JSA going after Zoom in Keystone City shortly after he had a run in with the League. Therefore I think the Sin Corps war took place during JSA #8 and was probably over by the time JSA #9 began, because otherwise you would be sure KC Supes would have been fighting the Sin Corps and or Prime.
I think the Sin Corps war took about 2 days or so, meaning there was probably 3 days between JSA #8 and #9, first day they were skiing, then they battled the Sin Corps, then JSA #9 starts.
Trying to match this up with JLA has been impossible so far. All I can think of is that it takes place after Monitor Duty (JLA #12) but prior to the Wedding Special. The Sin Corps Special part with the JLA might as well be JLA #12.5.