I was able to pretty much fix it. I knew there just had to be a way to make it work since the axis was successfully registering in Windows (and also confirmed with DXTweak2 & DIView). The following did the trick:
I adjusted the handbrake's preload almost all the way so that the handbrake's resting position is when it's registering around 70% in Windows. I then unplugged and replugged it back into my PC so that it would auto-calibrate with the new resting position as the 0% point. I then went to Windows controller and checked and by some sort of fluke, the handbrake now is able to be pressed all the way back registering 0-100% without any of the 2 buttons being registered. I knew from this point on it must surely work. I went into a few games (Dirt 4, RF2, AMS1, AC) and re-mapped the handbrake and, of course, it's now detected as an axis instead of a button in all the games.
In order to get the full throw of the handbrake back, I then adjusted the preload back to my original position, then disconnected & reconnected the handbrake from/to the PC. Once I did that, the 2 buttons of course started registering again but it doesn't seem to cause any problems in the games since those 2 buttons are not mapped to anything and the axis has already been mapped.
I wish we could reply to comments on Amazon because another person wrote in a review from just a week ago the exact same problem (although, funnily enough, not a single other review mentioned the issue). I'd love to show him this trick.
If Windows / DXTweak2 / DIView is recognizing the 0-100% axis then it seems to me it's working fine. On the other hand, no games seem to be detecting the axis but, I repeat, the axis is detected just fine by Windows itself. How does that make any sense???
I guess the problem is that games won't detect an axis when mapping controls if the axis is only registered until 20 or 30 % or so.