Bob, 
Its been a few years since I attended  a HP benchrest match. When I did the shooters using Sinclair/Witchita and sand bags/sinthetic were winning consistently against the unlimited class guys who used the one piece rests like tha Pappas. This was in the mid nineties. Manley Oakley was a friend of mine then and we used to hash over all the different types of rifles and rests. Even when Manley was in his eighties he kept up with all the latest hi tech gadgets. 
The Pappas rest is nothing new.

So I guess I still dont understand why you would use a one piece rest. 
One advantage I can understand would be the elimination of all shooting technique. All you do is mount the rifle in the rest aim and squeeze the trigger. That will cut down on required practice and a savings in ammo. 
Once you have the machine working all that is require is mastering the wind flags. I have shot in hundreds of BR matches over the years and still havent mastered the wind flags. This is a lesson that takes some many years to learn and others no time at all. 

I dont know of anyone other than Bev Pinney that is using a one piece rest. And even Bev's isn't solid but rather linked together to maintain distance. I tried to protest his rest off the line at Tacoma. Didnt work as nobody likes to rock the boat these days.

I've watched Jim Borton shoot BR, Tommy Mason, Jack Odor, Steve Garbe, Chuck Bordman,  Russ Weber, Pat Weber, Jay Scruggs, Ron Long, Earl Hines, Jim Luke, Jim Feren, Charley Dell, Gary Miller, Ron Long, The Hamiltons, Dave Purcell, and many other top BR shooters. not one of these shooters used a one piece rest. They all have one thing in common. They all practice and master the windflags. Ive shot a fair amount of trap too. Theres always the fellow who's trying to up his scores with some new shotgun or gadget. 
So, I still dont understand the advantage to the one piece rest. It sure is a cool looking contraption. I'll bet I could modify it into a usable drilling fixture.
Joe

I forgot to mention my daughter Aliann who when she was fifteen beat Bob Vail with a 247 at 100 with a .22. 

I was mighty proud of her that day. I coached her. I told Bob I'd coach him in the next match for twenty bucks. Bob offered me twenty bucks to leave him alone lol.   

Aliann used a Stevens 44 on sandbags. 


                                                   Joe. 

Great times Dave!  Enjoy while you can cuzz they grow up and get married.  Alianns off to Germany for four years come September. 

Hmmm, grandkids,,,,,,,,hmmmmmm.  



                            Joe.