My team consists of the following

SM SR Black Adam@200 primary attacker
SM UC Magog 2nd attacker
DC10 UC Green Lantern 2nd attacker/utility
DC10 R Flash tie up/interference
CE Dr. Fate utility/shutdown

The problem is this team is 36 pts shy and I will NOT use the IG or UB cause I do not like them.

Is there anything els I can do to get closer to 600?

Three questions:
Modern vs. Golden age in the tournament?
Do you only want Post-Johns era JSA?
Are there any particular characters in that lineup that are must plays for you?

Modern age.

I'm not stuck on any of them.

Is this a golden age or modern team? Starman works great for a JSA team. If you're looking for good Golden options I'd say Human Bomb from AA and Uncle Sam for CR.

If you have the jet and DC 75th wonder woman 051 than this is what you should do

200 SM054E Black Adam
93 D10A011 Green Lantern
100 WKD-003 Dr. Fate
106 BMV003B Invisible Jet (Piloted)
100 AN051 Wonder Woman
599

That green lantern is perfect for purple ray cuz he great at range and he has willpower. The jet can carry the whole team for monuverability. And nobody on the team is a slouch.

Golden Age of Comics
100 WKD-003 Dr. Fate
120 AN050 Superman
100 AN051 Wonder Woman
93 D10A011 Green Lantern
86 D10A018 The Flash
50 BMV003A Invisible Jet (Autopilot)
50 AN012 The Atom
599