Bob, I have lost the few pictures of American made half stock, pistol grip rifles that I was able to find. I can not seem to recover them. They did not have the well defined pistol grip like the Swiss or English though. More of a sweeping grip - kind of like the bag handle on the Hawken that Stoner shows. My rifle is not an exact copy of any American rifle I found, but more of a mixture of Swiss Match rifles, Rigby's or Gibb's styles, with a small amount of American influence thrown in. In other words, a fantasy gun.
In my opinion, the reverse/backwards - rear fire double set trigger has a slight advantage of firing hand placement. It aids in keeping the firing hand/arm a little further to the rear and thereby keeps you from pushing the firing hand/elbow/shoulder forward and out in order to reach the front trigger. I guess a more compact stance. The same feel can be accomplished by adjusting the LOP, but something does feel better and seems more stable with the rear fire trigger. An easy way to experience the difference is to shoulder a rifle with the standard double set trigger. Simulate your firing with the front trigger and then simulate with firing the rear trigger. I am able to get this same control/feel with my half stock builds with a single trigger.