In regards to the OP: A slight boost would be when given a POWER action your breakaway roll is -1 (or change Charge and RS to -1 breakaway and change HSS to only a +1). So for basic situations ; you'd need a 5 or 6 for Running Shot/Charge breakaway and a 3-6 for HSS breakaway, gives another ~16-17% chance of failure to consider.

Wonder Woman shouldn't need to breakaway but the Hawkgirl team up is her friend (thought it was needed because of old plasticity rules).

Agreed. Quick fix would be to drop giants from Great Size so they don't get the range bonus but keep the close combat bonus (Giant Reach).

Actually what you say in your last sentence is wrong, because you would not be able to use HSS, Leap/Climb, Running Shot, Charge since you can't give a character 2 costed actions in the same turn ( POWER and MOVE or POWER and POWER). Then they become instantly garbage not valuable (Leap/Climb gives you the +2 BREAKAWAY only if you activate it and that requires you to assign a MOVE).
Plasticity and HSS's bonuses to BREAKAWAY would be the only ones not affected by this change because they get that bonus regardless if you are using them or not.

This is absolutely true, and a fairly obvious oversight on my part.

This a fantastic idea. Way better than my proposal.

I think a new ability for characters with 0 Range get a +1 Breakaway and -1 for Opposing Breakaway would be interesting to try.

That or make close oriented characters better defensively. Maybe more 19 Def for them. Or at least 18.