Pressure "IS" directly related to payload & velocity, just not peak pressure. The pressure curve can be Re-Arranged by varying the burning rate of the propellant. Powders used in the .410 for even normal loads are already slower, more progressive than those used in the larger gauges except for possibly a few extreme Magnum loads. As you have a lot smaller powder charge to ignite in a much smaller space bloopers are likely not going to be as critical in the small bore as in larger gauges. The primer is putting out the same amount of "Fire" to light the smaller charge. While 7625 is a Slow powder in a 12ga it is a Very Fast one in a 3" .410. It's all relative, but yes when you look at total pressure its always going to be higher in the .410.
The good part is the .410 will handle a higher pressure than will the larger bores.
Exactly. Related, but not directly proportional.
SRH