Experiments included bullet diameter in the '06 and tumble lube in the 357.
Liquid alox / as-cast 0.314"   average 2.7", 1575 fps.   There was a grey wash near the muzzle but nothing serious.
Liquid alox / 0.309"   average 4.5", 1625 fps.   Again there was a little grey wash near the muzzle.
Rooster Jacket & moly / 0.309"   average 3.1", 1610 fps.   The usual grey wash near the muzzle.
Rooster Jacket & moly / 0.309" / dacron   average 4.2", 1590 fps.   Grey wash near the muzzle.
Conclusions   The 0.314" bullet outperformed the 0.309" bullet with liquid alox.   With Rooster Jacket & moly, the 0.309" bullet shot just as well as the 0.314" bullet (at the previous range session).   The dacron did not help in any way.   None of the loads gave great accuracy, but this was a test of lube and diameter, not a quest for the ultimate load.   The bottom line is that both liquid alox and Rooster Jacket & moly gave barely adequate lubrication at 1600 fps with a plain base bullet.   The oversize bullet did no harm and seemed to help in the case of liquid alox.
As-cast 0.312"   average 4.2", 2600 fps.   There was a grey wash near the muzzle.   The barrel condition never changed and the POI never changed.
0.309"   average 2600 fps, no accuracy data because I never succeeded in keeping all 5 shots on the target and it was a pretty big target, too!   Grey wash near the muzzle.
Conclusions   Last year I did a similar experiment with 0.312" vs. 0.309" and got similar results but later learned that the case neck was squeezing the bullet diameter down as small as 0.304", so I made a new M-die spud that was big enough to prevent bullet damage and repeated the experiment today.   The 0.312" bullet clearly outperformed the 0.309" bullet.   Accuracy wasn't anything to brag about but, hey, at least it was a group and not a pattern.   The chamber is able to swallow a 0.318" bullet, so the next test will be 0.312" vs. something even bigger.   This was the first time I had tried adding moly to wonderlube and also the first time I had tried the 2-angle grooves, so the jury is still out on those two items.   There are many more experiments I would like to try with this load but you have to start somewhere and diameter seems pretty important.
Rooster Jacket & Moly   Average 7.5".   Some light streaks near the muzzle but not too bad, and it didn't get any worse.
Liquid Alox   Average 6.0".   Barrel condition was identical to the Rooster Jacket & Moly.
Rooster Jacket   Averaged 6.4".   Barrel condition was just a tiny bit cleaner than the other two lubes.
Conclusions   At the last range session I tried a similar experiment except with air-cooled WW at 1300 fps, and got some leading that seemed to get worse as more shots were fired.   This test was to see if less velocity and harder bullets would help.   While there was still some minor leading near the muzzle, it was not as bad and it did not get any worse as the test progressed.   The bottom line is that all of the tumble lubes gave barely adequate results at magnum velocities providing the bullets were heat treated.   By comparison, this bullet will average less than 5" with H110 powder and a conventional lube.   The next test will be a shootout between H110 and WC820.