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I'm not sure about that, Hal was pretty much same in Dark Knight Strikes Again. Maybe the difference might be that Master Race was "bigger" than previous two stories so other characters simply got more pages and more stuff to do.
I had to be convinced to read DKIII by a friend who literally had to shove his copies into my hands because I was so disinterested in reading it after the cocaine-fueled shitshow that was Dark Knight Strikes Again.
However, I kinda dug DKIII and the follow-up The Golden Child was even better.
Master Race is basically about bunch of Kryptonians trying to take over the Earth. Few Kryptonians visit Hal. Initially they are afraid of Hal due to his power, but when they realise that his power comes from the ring they quickly severe his hand with a heat vision when he wasn't expecting it. And they throw his hand, with the ring, away. Later in the series Hal finds his hand and kinda connects with it mentally? It does not get reattached to him, but it floats in front of him and he gets his full powers back. Eventually he runs into same Kryptonians and obliterates them. From what I remember its not even a fight, they get blown away in one panel and thats that.
Here's a creepy shot of Hal controlling his hand...
dkiii-hal-jordan.jpg