I crawled the world looking for info on the GH6, GH7, or GHC module for use with the DM10. All I found were vague claims that somebody somewhere somehow had some success with the combination, and everything worked.
I decided to gamble on the GHC module with a real hi-hat stand and the stock cymbal. As far as I can tell, it's exactly the same module as the GH6, minus the cymbal.
After messing around with the settings and the physical setup extensively, my conclusion is that this combination leaves something to be desired, but it is a vast improvement over the stock hi-hat pedal. I can't trigger the splash with any reliability at all so far, but closed is much more reliable, and the continuum between open and closed is easier to control in a musical way.
The stock "real hat" pedal calibrates to about 80 at open and 0 at closed, whereas this GHC module calibrates at 38 open and about 5 closed. The range of values is much more limited, and I feel this may be part of the problem. I'm still trying to see if I can work out how to get the splash to work. If I do, this will be just fine; assuming it holds up over time.
If not, I guess I will try the Pintech next, and if that doesn't suit me, I'm probably going to have to try my hand at making something from scratch. The "real hat" pedal is awful, and the concept of using a real hi-hat stand with the DM10 is definitely viable, but I don't know if this solution is going to turn out to be my final destination or not.
For $60, I feel like I definitely got a massive improvement, and I am not considering switching back. This puts me in a happier place than almost everyone who has ever reviewed the X-Hat, so I think this was a good way to go.