I bought a ZKK600 (30/06) in 1974 and really liked it. It shot quite well "out of the box" but , like any "bedded in the wood" rifle was inconsistent shooting very well one day and not so well the next. I decided to glassbed.
First time around I bedded it full length. I figured since BRNO went through all the effort to incorporate the forend screw, I would continue to use it. The rifle shot better but with one major flaw. If I shot a 5 shot group, it would be a decent, round group. If I then allowed the rifle to cool only the length of time it took to walk up and check the 100 yd target and walk back, the first shot of the next group would hit about four or five inches high, the next shot a couple inches lower and the third shot back at the original point of impact. From there, if I continued to fire, all subsequent shots would group in that area. If I allowed the rifle to cool completely, the group would form where it should have as well. Every other bolt action rifle I had worked with, I had floated the barrel so I decided to do the same with my BRNO. I did this by simply removing the necessary material from the forend and removing the little block into which the forend screw was threaded. I then glued the screw back into the stock just to fill the hole. It worked perfectly and the "walking point of impact" problem was gone.
At the same time, I noticed the barrel had a noticable tight spot right at the location of the rear sight boss. Although accuracy was pretty good at around 1 inch or so at 100yd, I couldn't stand the thought of that tight spot so I cast a lead lap and lapped the barrel with some 400 grit clover compount to eliminate the tight spot. It took some time, by the way, but I got it done. I cast a second lap and polished the bore with JB compound to finish it.
After this the rifle was very consistent and was, in fact one of the best shooting factory rifles I have ever had. I shot many 5 shot groups which were well under 3/4 inch and even some under 1/2 using 180 Sierras.
In the intervening years I have become solidly convinced that, if you want a barrel free floated, it should be floated all the way. Bedding just ahead of the receiver has always resulted in a tendency toward vertical flyers. Others may, of course, disagree and are welcome to do so!
By the way, the inserts in the BRNO stock are not, peoperly speaking, pillars. A pillar is bonded to the stock so it becomes an imtegral part of the stock. These are not and are therefor a spacer rather than a pillar.
Regarding the use of cardboard shims; I recall an exchange between Alex Bulman and his brother-in-law, Harlan Govett. Harlan was fooling around with his heavy bench rifle. He had a dial guage set up on the barrel and was placing pieces of match book cover at various strategic locations within the receiver area then tightening the screws while watching the guage. Finally satisfied, he said, " I think that'll do it!"
Alex replied, "Well, if it does, I've wasted a lot of my money!"
I agree with Alex. The placement of cardboard shim will not prove or disprove the merits of free floating the barrel. It will only prove or disprove the merits of the cardboard shim. Regards, Bill.