Originally Posted by FBinNY

OK, so a quick analogy so you know where I'm going. Imagine you're hanging from a rope tied to the hands of a tower clock. At noon and six the hand won't move no matter how you hard you pull the rope. As you approach 3 or 9 you reach peak leverage, with everything in between being less.

So, now (if you can see it) look at the brake's cable actuating arm at the point the pads are engaged. (close lever and tie it so you can focus on the caliper). I suspect that it's now comparable to the clock's hand having over traveled and now nearing 5 O'clock.

If so, the fix is fairly easy. Reposition the brake (shim if needed) so the moving pad is close to the rotor with the cable fully slack, Then adjust the fixed pad to proper minimum clearance, rather than taking up cable with the adjuster. From there it's just some fine tuning. The brake should now work so that the arm is closer to 3 o'clock (90 degrees to cable's line of motion) and you'll get maximum leverage at the point of brake engagement.