A deep-seated bullet in the 357 and Rooster HVR in the '06.
18.2 gr. H110   5.20", 1278 fps, 43 ES.   Quickload predicted 1265 fps at 34,580 psi.
18.4 gr. 296   4.93", 1287 fps, 51 ES   Quickload predicted 1261 fps at 32,009 psi.
Conclusions   I was hoping to use a bullet that seats deeper than the 35_PB_160_snub.   Deeper seating means less powder is required to reach the same velocity.   It also makes room for one more grease groove.   It also gives the case a better grip on the bullet which might improve ignition with slow powders.   Accuracy was on par with the 35_PB_160_snub, so I'm pretty happy, but naturally, I want to experiment with yet another deep-seated design.
Most of the following loads had two grooves on the nose left empty to act as scrapers.
0.312" ogival nose loverin   average 1.88", 2725 fps, 26 ES, all 9 shots 3.84" 50 ES.   Hey, it wants to shoot!   The first shot was the fouling shot in a cold, clean barrel.   Minus the fouler leaves 8 shots in 1.87".
0.302" x 0.312" tapered truncated cone loverin   average 3.65", 2758 fps, 34 ES, all 9 shots 4.88" 73 ES.   This gun is not liking tapered bullets.
0.302" x 0.312" tapered truncated cone loverin, Neco P-check   average 8.3", 2761 fps, 35 ES.   I quit after 6 shots because it obviously did not want to shoot.   No significant improvement in velocity or ES, either.   A couple of the P-checks were recovered downrange and they looked almost new.
0.302" x 0.314" tapered truncated cone loverin   average 4.90", 2760 fps, 42 ES, all 9 shots 5.71" 57 ES. all 9 shots 4.06" 44 ES.   The tapered 0.314" was even worse than the tapered 0.312".
0.312" ogival nose loverin, 1 Turn forearm pressure   average 2.65", 2710 fps. 22 ES, all 9 shots 4.06" 44 ES.   I installed a bug hole tuner at the tip of the stock that allows me to either free float or apply various degrees of upward pressure by turning a screw.  It didn't help, so I'll go back to free floating.
Conclusions   I don't know why the tapered bullet's don't shoot, but for now I'll have to accept it.   As long as a good lube is used, gas seal doesn't seem to be an issue with these loverins, judging by the velocities.   From here I'll continue to fine tune diameters, lubes, and seating depth, and maybe hollow point the loverin to get the velocity up.