For single shots, my recommended receiver is the BAT model M 1.55"x8.5" with the stainless steel 40 moa rail base which I modify the receiver and rail to accept 4, 10-32 tapered head mounting bolts.
I have to do this with my PK brakes or the rail WILL work loose when shooting. I have also had to use two sets of scope rings, one to control recoil energy, one to control the extreme deceleration caused by the muzzle brake
. I am fine dealing with that to have the very low recoil.
Stocks, my preferred stock is the McMillan A-5 if going for a lighter rifle weight, if weight is not a real issue, I really like the new A-5 SuperMag stocks as well. Joel makes a great stock as well if you like a top end laminate stock.
Barrels. I have used alot of Lilja barrels. THey shoot amazingly well. They are pretty tight bored so they will limited velocity slightly but accuracy is great. Kreigers are also performing very well and they stand up to this extreme chambering a bit longer then the softer button pulled barrels.
. Simply put, I feel my 5 port PK brake is the best there is but I designed it specifically for this class of chambering. In a 16 lb rifle, recoil is about like a 270 Win in a sporter weight rifle and thats driving a 300 gr SMK to nearly 3400 fps.
If you want a repeater, THe Lawton is a good choice but as mentioned, it is what it is and there will be some issues with it. Mainly cosmetic. It works, it works well. I just sold my personal 375 AM repeater that used the Lawton and Chey Tac DM system. McMillan Super Mag stock and Lilja 33" barrel. She punched a 4.4" ctc group at 1780 yards driving the 350 gr SMK to 3300 fps.
The 4.4" group is the top triangle. The bottom hit is from earlier in the day in intense mirage and its the only hit I got on steel until the mirage went away, they it was in trouble.
Weight wise, I like a rifle in the 18-19 lb range for serious long range shooting. That is where my standard Xtreme Heavy Sporters come in at with NF scope and Harris bipod.
I also make a lightweight version of my Xtreme Heavy Sporter that uses conventional stocks, all steel barrels and the BAT single shot that comes in at 16 lbs with scope and bipod. Here is a pic of this rifle. This is a customers rifle, just got a report from him that he was finally able to get out and test it and shot some sub 1" three shot groups at 400 yards. He was really itching to stretch things out.
This rifle has the standard A-5 stock but has the adjustable CP. IF you went with a 50mm or smaller objective scope and mounted it as low as possible you could get away without the adj. cp and cut even more weight off the rifle.