>>1820538There's two kinds of centerpull brakes. The most common is center-mount using a single bolt--fairly easy to set up, but middling performance. They're out of style, and you described one of the main issues. Using spherical/leveling washers is a good fix for it.
There's also centerpull brakes that mount to canti-like studs. Pretty often it's old Mafac brakes. And these are awesome, peak rim brake. The pivots are much closer to the brake pads, so there's less flex in the caliper arms. Check it out.
>>1820547Installing in-line adjusters changes canti brakes from "ugh, so fiddly to set up" to "why don't more people use these??".
As far as I know, Shimano is the only company that sells a "rated for brakes" adjuster, but I've used the Jagwire ones for years with no issues.