Ok, I took those measurements, and a closer look at my machine.
From flat to flat, the hex for my machine is nominally 30mm. I didn't measure the machine, but I'm guessing that will be close to 30mm, and the tool is undersized by about 0.3mm for clearance.
The "groove" is just about 3mm deep, and has radiused corners (one measurement is between the bottom of the corners, the other is between the tops).
The 52mm (plus a radiused shoulder that's not clearly drawn in of about 4mm) round section at the back of the tool is absolutely required.
I know this, because I grabbed a tool from my Bosch Brute (which is hex all the way back, but looks to be the smaller 28mm flat-to-flat size that HF is using), and it does not go into this machine sufficiently to reach the hammer. Looking into the business end, you can see that there is a round chamber which the tool must fit into behind the hex (it looks a lot like an air chisel).
Hope this gets you on the right track.