Another thought:
While all of this advice is well and good, here is a simple solution. Consider making the size of your starting hole larger. If you start with a bigger starting hole, then the broach will fit down into the hole further and you may not need to buy a new arbor press or create a new setup suggested by the brilliant people in this thread.
For instance, if you are creating a 1/2" Hex hole, start out with a 0.520" hole instead of a 0.500" hole. For most applications, I contend that you don't need the middle of the hex flat to transmit the torque, only the outer 1/3 of the hex flat. (If you want to test this, put a hex wrench on a piece of aluminum hex stock. Hold the stock in a vice and torque the wrench until the aluminum is stripped. You will see that the middle of the hex flat is unused. This is actually the same thing I did when designing the churro many years back.)
Here is a pic to show what I mean:
Hope this helps!
Andy B.