Thanks for the info. What do the back sides of these studs look like? On mine, the stud is completely loose in the hole. You can push on it and it will go all the way up into the hole and when you let go it will fall back out through the hole but it will not come all the way out. It just hangs there. You can also spin it all the way around. It almost feels like it had a nut or a head of some kind on the inside of the transmission that held it in place. Maybe ours are made differently If I'm reading your post correctly, your studs are threaded on both ends and screw up into the trans. I don't think mine work like that When you push up on the stud, it actually feels like if you pushed it far enough into the hole, it would end up inside the trans! Like there's no end to the hole it comes out of."
I checked the Buick parts book. The reaction flange looks the same as my 55. The studs are the same part number from 49-56. See photo. Part E and part U. I would say you would need to pull it out and install a heli coil. If you have never done it before I would find some one who has or practice on something else. If you do it correctly it will be a permanent repair. Mud