I have a model 21 Varminter in 223, I had a Phoenix in 204 but sold it, I have a LVT stock for a 57M, I also have a Jackson Hunter in 22 l.r. and sometimes for bench shooting I put the 57M into the LVT stock. The Varminter, Phoenix and LVT all use the same stock design but are inletted for differnet actions just as the model 22 uses the same stock but inletted for the model 22 action. I also have a Classic in 222 which is what I originally purchased the Fore-end Adaptor for but ended up using it on my Varminter stocks some times.
I have not experienced any "unexplained" flyers from any of my Coopers, either with or without the fore-end adaptor. The Classic style stock is more difficult to shoot from the rest because of the narrow fore-end. I purchased the adaptor to make it easier to shoot and I ended up using it on the other stocks from time to time.
The fore-end adaptor makes it easier to shoot any of them becasue it has a 3inch flat bottom on it and of course it lessens the stocks tendency to want to roll, or not be in the same position, each time. Prior to purchasing the fore-end adaptor I purchased a Protektor fore-end bag that closely conforms to the stock design and I can shoot it as well as if I were using the fore-end adaptor but I do have to work harder at it. With the fore-end adaptor I use a flat "lobe type" bag and when I am not using it I use the Protektor bag that fits the Varminter style fore-end.
I do not know exactly what you are referring to when you speak of "unexplained" flyers but generally speaking "unexplained" flyers can be overcome by good bags and rests, good bag set-up, doing the exact same thing shot after shot, and wind-flags. I use three flags on a 100 yard set-up, if a person is not used to using them it takes quite a while to figure out what they are telling you, but it is hopeless to try to shoot consistent small groups without them.
All of my Coopers shoot between 1/4 and 1/2 inch five shot groups at 100 yds (excluding the 22 l.r. which generally shoots under an inch at 100) they are all consistent and predictable. I have shot some groups smaller but very rarely have I shot any larger than that.
I have adjusted the triggers on the 223 Varminter to 10 ounces since I generally use it for bench work, and my Jackson Hunter and Classic in 222 are both set at 18 ounces because they are more of a field gun.
If you want a lighter trigger the Cooper can be adjusted safely to the levels I have mine set at, or Jard has a lighter trigger available. I have shot a Cooper with the Jard trigger and it felt as good as the Jewell trigger that I have on a Remington, but that was my limited experience with them. The Cooper trigger adjusts the same as the older Rem 700 triggers, any smith who is good on Remington triggers should be able to get yours factory trigger to these levels, if you want to go lower then the Jard is the best option.
I will not pretend to tell anyone that the Cooper is a benchrest rifle but they are a great varmint rifle, which is what they are sold as, I use mine in the local benchshoots and win my share with mine against some pretty serious bench rifles though. The thing that I like about them is that I can use them for varminting, my main passion, but still can shoot them in local bench rest matches with at least somewhat of a chance of placing, wheras it is difficult to take a pure benchrest rifle varmint hunting - it is a compromise I am happy with.
Take care and good shooting, enjoy them for what they are.
drover