I'm still working on fixing mine. I got the broken screws out without destroying the boat but still have some work to do to fix the hole and get everything back together.
The first image shows the 10-24 machine screws broken off in the holes. The second shows what's left of the two screws after using a roll pin to extract them. As you can see the first one came out okay, almost miraculously, after chucking up a 1/4" roll pin and running it in reverse over the broken machine screw. The second one was a lot more frustrating. At first it bit a tiny piece off the screw. Then I couldn't get the roll pin to bite any more so I tried cutting some left handed teeth in the fresh end with an angle grinder. That made it cut better but it still wouldn't bite. I switched to a smaller size roll pin and that took a ton of force to get around the screw and as soon as it bit down it sheared off another tiny piece of the screw rather than turning it out of the hole. This happened with both ends of the smaller roll pin before I went back to the sharp end of the first pin and pushed harder faster and more angrily. After smoking a ton of resin and boiling a lot of my sweat that kept falling on hot metal, the last inch or so of screw came out.
As shown in the third photo, the screws are out but the holes aren't perfect. There is probably 1.25" of good threads on the better hole and 1" on the worse hole. I had to run a tap down the bad hole to clear the threads.
Now I'm trying to decide how I'm going to re install everything. I'm planning on using new 10-24 x 1.5" machine screws and the existing holes.
Option 1: I could just fill all the extra space and the whole recess with butyl tape and trust that 1" of those old threads is good enough (I've read that [in steel at least] tapping more than 2.5 diameters of hole gives no additional pull out strength).
Option 2: Or I could spray the new screws with silicone lube, fill the holes with marine tex. coat the bottom of the brackets with Vaseline and install the center board before the epoxy starts to setup and pray that the bolts and bracket don't end up bonded to the holes.
Option 3: Or I could attempt to cast new threads in the bad holes by spraying the screws with silicone, filling the holes with marine tex and inserting just the new screws (no bracket) and letting that cure before backing the screws out again and putting the bracket on.
I don't like option 3 because if the machine screws seize in the holes, I'm back to where I started (although if I'm lucky, I can back them out with vise grips and avoid shearing them off. Has anyone tried casting machine screws in marine tex?
I don't like option 2 because there's a chance I'd end up epoxying the bracket to the boat.
I don't like option 1 because the centerboard bracket takes a lot of pull out force caused by the long lever arm of the centerboard prying the bracket out of its holes. I'm just not sure if I can believe that 3/4" = 1" of resin or epoxy threads are good enough to resist the board being ripped out of the deck. And if I lose the centerboard downwind of the dock, I'd be screwed making any windward headway.
While I think about that, I can start prepping to fix the chips and scrapes on the bow and the missing chunk of centerboard from this same little incident.