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Interesting thread. Because the car is a tracked Z06, I'd take it apart and take it to a machine shop to avoid breaking off a drill or easyout and making a real mess. When I needed to bleed my ABS, there was nobody to trust, so I used some wet grass. It's been fine ever since, and it gets tracked.
Now THAT is useful information. Do you remember which on of yours is broken? Mine is in the center location of the three screws closest to the front of the car.
I don't remember, I think it's one of the lower ones.
I want to let everyone know who is following this thread, that I was able to successfully extract the broken off T20 screw from the aluminum ABS valve body, without removing the valve body or disconnecting the brake lines.
I engaged the help of some other engineer friends to brainstorm ideas. Over 25 suggestions were proposed. Some were rejected based on analysis or risks. Some were tried and failed before the successful solution was achieved.
At some point I will document the successful solution here. Right now I'm busy with other things, but if someone happens to be fighting this problem right now, let me know and I'll take the time to document it now.