The Pederson rifle did indeed lube the cases, but not with wax, IIRC. It had oiler pads built into the magazines.
Varmint Al has a finite element
model showing case stress and boltface thrust on firing on his web site. It shows that within the coefficient of friction of common petroleum-based lubes, the brass still sticks to the chamber wall, just not as well.
You can test this very simply. During normal firing of a FL resized case, the firing pin pushes the whole cartridge forward against the headspace stop (shoulder, for most of us, but rim or belt in cartridges with those features). As the powder starts to burn, the cartridge is in this forward position. In a high power rifle, the pressure builds far enough to expand the case web (walls) and by simple friction will stick them to the chamber walls before the bullet is released from the neck. Only after the bullet is released by the neck does the pressure try to push the case rearward. At this point, if the case has stuck to the chamber wall, the casehead can move rearward only by stretching the web where it meets the casehead. This is the cause of the thinned ring of brass that eventually results in casehead separation.
If cases didn't stick, thinning and casehead separation would not occur. It is why you don't see the problem in most pistol and lower pressure chambering that do not have enough pressure to stick to the chamber wall. The threshold is usually in loads with around 30,000 PSI peak pressure, but also depends on the case geometry. It is also why lower pressure pistol rounds never needing the cases trimmed. They can actually shorten with resizing, which flows the brass rearward.
Al's analysis shows that some old beliefs about case sticking are false. Increased boltface thrust does occur, but it isn't terribly significant until the coefficient of friction is greatly reduced. Merely polishing a chamber does not reduce friction enough to make serious trouble. In his modeling, a normal chamber boltface thrust of around 4500 pounds is increased to about 7600 pounds when the coefficient of fricition is reduced to 0.01. That is the half the coefficient of friction of molybdenum disulfide (moly). By comparison, a greased chamber COF is about 0.11. That only raises boltface thrust about 8%. If your bolt lugs are not lapped or are otherwise uneven. that can increase stringing along the closed lug axis. With a blueprinted gun, it shouldn't matter much, as long as it is uniform.
As with the Pederson design, a lubed case will help extraction in a self-loader because the pressure drops enough for the lube to break friction with the chamber by the time extraction occurs. I am more inclined to try polishing the chamber first, and see whether that doesn't helps enough? I have a new M1A barrel, and I will try this when I chamber it. All lists COF for very rough down to polished chambers as going from about 0.55 down to 0.19.
I have heard of benchrest shooters getting 50 reloads from a case. These would be cases neck-sized only until they get too hard to fit. At that point the benchresters use a special die called a bump die. It pushes the shoulder back without narrowing the web.
The forward flow of brass mentioned earlier accumulates where the shoulder and neck meet. The effect is to narrow the base of the neck by forming a thickened brass ring inside it. This is commonly called, "the dreaded donut." It must be removed with an inside neck reamer. That becomes a regular step for benchresters, done when they trim a case.