MM,
What you describe makes perfect sense. Part of the reason is start pressure. You may have noticed a fired case's neck is normally expanded to the chamber neck diameter except right at the edge of the mouth, which remains curled in? That is because, as pressure builds, the case expands to fill the chamber diameter, but the neck has to expand from where the bottom of the bullet bearing surface is squeezed by neck tension, then forward from there to let go of the bullet. As that forward rolling neck expansion arrives at the case mouth, it starts to bleed gas out, so the pressure differential between the case and the outside is lost, and is thus unable to expand the lip of the mouth like the rest of the neck.
What's important about that is, during the forward rolling expansion of the neck the bullet largely stays put. That allows pressure to build. At its release, the bullet has gas blowing past it via the edge of the case mouth and into the bore, but because the pressure has already grown, the bullet pops forward into the bore pretty fast. It's like a champagne cork that way. During the short time there is gas bypassing the bullet, the pressure rate of rise in the chamber is slowed, but once the bullet moves forward enough to obturate the bore, it continues building well.
If the bullet is shallowly seated, pressure won't have built nearly as much by the time the bullet has been released. This means the bullet moves toward the throat more slowly while allowing gas bypass. If the distance it has to go is short, the gas bypass period is still pretty short, and pressure may then go on to build normally. But if the distance the bullet has to travel to obturate the bore is long, gas bypass from a shallowly seated bullet will go on for a relatively long time, which greatly reduces peak pressure. A little difference in neck tension, a little shift in the powder position at ignition, or anything else that might slightly change the exact pressure at which the bullet is released and at which gas bypass commences will then have a greatly exaggerated influence on final peak pressure. This is due to varying the initial burning rate of the powder by varying the pressure via the amount of gas that bleeds off. Powder burning rate varies greatly with pressure, but especially greatly at pressures barely adequate to keep the powder burning. In other words, it's like taking all the factors that cause normal variation in velocity and magnifying their effect on peak pressure several fold.
Below is a graph taken from data in the 1965 U of Michigan study of cartridge pressure. It is for a round nose bullet in a .30-06 case. The round nose bullet is almost 0.9" long and the short ogive means it doesn't have to stick out very far to touch the lands. As a result, even when the bullet is touching the lands in the Springfield '03 barrel used in the tests, it is still pretty well seated into the neck. As it is seated still deeper, gas bypass that did not occur when the bullet touched the lands starts. and becomes increasingly greater. This drops starting pressure and thereby lowers the resulting peak pressure because the powder is burning more slowly when the bullet is getting into the bore. Once the bullet is seated deeply enough, the decrease in peak pressure due to gas bypass starts to be offset by the decrease in case volume the bullet has under it. Once that volume gets small enough, start pressure is assisted in its rise by commencing to burn in the smaller volume, and that raises pressure again.