Badger barrels were at first single cut, as per what Ernie learned from Boots Obermeyer. But then,for Most of the Badger barrels
he switched to single pass Broach Cutting them for faster production.  Still good shooting barrels such as those on the Browning BPCRs. 
Kriegers are still single cut. Exlt barrels.  John Krieger has more recently added the more popularly priced Criterion barrels which are, I believe button rifled. The Criterions are are almost totally finished/blued or parkerized and ready to 
fit to '03 Springfields, Garands, Carbines and even Krags-for Vin Mil matches

You might look at the blanks CPA offers for extra cost over the good Douglas barrels, Shilen, Bartlein and RKS? I've personally never used an RKS in a build. Someday, I'll try one and I also would like to try a BRC barrel some time. Good luck with it.

Rifles used by best 50 shot cast bullet shooters with single shot rifles in last twentyfive years. Only shooters that have shot 1240 or more out a maximum score of 1250.

1240 Jerry Hartwig 2015 Modesto, California
        120 grain Mos 10:1 Douglas 20:1 alloy (.25-20 WCF) 20X Lyman Targetspot CPA 44 1/2 AA4100

1240 Jan Pritchard 2010 Modesto, California
        208 grain Darr 16:1 Darr (.32-40) Unertl 20X Falling Block Works AA#9

1240 Lowell D. Hamilton 1996 Raton, New Mexico (Pistol Match)
        213 grain Paul Jones 14:1 Douglas (.32 Miller) Leupold 36X Miller DeHaas AA#9

1241 Ron Yatso 2015 Tacoma, Washington
       230 grain Paul Jones 14:1 RKS Gain (.32 MS) Night Force ?X Miller DeHaas AA#9

1241 Gerald Miller 2010 Tacoma, Washington
        227 grain Paul Jones 14:1 RKS Gain (.32-40) Weaver 25X Ruger #3 H108

1241 Dave Purcell 2010 Raton, New Mexico
        220 grain Mos 14:1 RKS Gain (.32 MS) Redfield 32X Miller DeHaas H108

1241 Earl Hines 1996 Raton, New Mexico
        220 grain Brewer 14:1 RKS Gain (.32 MS) Unertl 36X Miller DeHaas H108

1242*Jeff Schultz 2011 Etna Green, Indiana.
         217 grain Borton-Darr 14:1 Shilen (.32-40) Weaver 36X Miller DeHaas ?Powder

1243 Tommy Mason 2010 Spruce Grove, Alberta
        206 grain Paul Jones 14:1 RKS Gain (.32 MS) Unertl 32X Miller DeHaas H108

1243 Jim Borton 2007 Etna Green, Indiana.
        215 grain Borton-Darr 11.5:1 RKS Gain (.32 MS) Sightron 36X Miller DeHaas ?Powder

1244 Rick MacHale 2016 Raton, New Mexico
        230 grain Paul Jones 12:1 RKS Gain (.32-40) Lyman 20X CPA Stevens 44 1/2 Win 296

1245 John Schauf 2021 Tacoma, Washington
        210 grain Schauf Round Nose 14:1 Shilen (.32-20) Night Force 42X CPA Stevens 44 1/2 AA4100

1245*Dale Reynolds 2011 Warsaw, Indiana
         ? grain Borton-Darr 10:1 Pac-Nor (32-30 Rem) Sightron 36X Reynolds Custom Action ?Powder

1245 Dave Patterson 2007 Nine Mile Falls, Washington
        236 grain Paul Jones 11.5:1 RKS Gain (.32 RKS) Burris 24X Miller DeHaas H108

1247 Donn Hanks 2016 Phoenix, Arizona
        198 grain Mos 14:1 RKS Gain (.32 MS) Weaver 36X Hoch AA#9

1249 Jack Odor 2011 Raton, New Mexico
        207 grain Mos 14:1 RKS Gain (.32 MS) Leupold 36X Miller DeHaas AA#9

Joe you could help change that. 
They actually haven't been around that long and they could use your abilities and your support to help them out.

Accuracy from a RKS barrel when you have selected an appropriate bullet length for your barrel's twist, once you know how to properly call the wind and have learned how to properly seat your bullet to the correct depth with an adjustable breech seater  and you have determined the proper powder load to minimize your barrel vibrations. Not to mention proper bench technique. Hepburnman PM me if you would like further advice.

Looks like you could learn something John if you were ever to listen - but it appears you believe you have everything figured out anyways (except RKS barrels). 
However ten (62.5%) of the TOP sixteen 50 shot benchrest shooters seem to have figured them out.
And only one Douglas barrel made it onto the list with the lowest score of 1240.
How come you have never successfully shot 1240 or better John in the last twenty five years?
When you have outstanding benchrest technique and a Douglas barrel.

Thankyou all for the advice, buying a barrel is quite an expense when you live in Australia and have to get an export permit to get t out of the USA which costs nearly US$ 400. On top of the permit costs there is also freight etc plus clearance costs when it arrives here.  I'm speaking from experience, not what I have been told it might cost. I will make enquiries with CPA as to the cost of fitting a barrel to my Hi Wall action and chambering it as well. I am happy with the Krieger barrel in my 441/2 that CPA  put together for me, perhaps at my age I may not see any improvement in accuracy worth spending a grand on. I feel sorry for barrel makers as it only takes one bad one to slip through and with the advent of social media the bad news can spread like wildfire. I don't know if it's true or not but I read somewhere that Harry Pope had a way of testing his barrels before they got sent out, and if there was a problem he would rectify it before shipment, don't know how true that story is though. All my dealings with CPA have been very positive and that is where I will start this journey.
Thanks again.
Mike.
PS  My 80th birthday is in January, I can supply my address to  anybody wishing to send expensive gifts. (just hoping ) .