Correct me if I'm wrong but KPI is determined by comparing the center of contact patch to were the center line of the ball joints would hit the ground (caster angle). As that distance (scrub radius) increases -that upper angle that I've labeled KPI increases.
(Scrub radius can also be affected by wheel back spacing.)
I very well could be using the wrong terminology but when I have a minute I'll draw diagram of what I'm trying to articulate.
KPI (king pin inclination) is the angle of the line drawn through your upper and lower ball joints (or king pin) relative to vertical
when viewing from the front or rear of the vehicle. The difference between where that line intersects the ground (scrub pivot point), and the center of the tire contact patch on the ground is your scrub radius. So, what you're calling KPI is actually the scrub radius.
Caster angle is the angle of the line through your ball joints relative to vertical
when viewed from the side, so it is different than KPI, although they reference the same line.
Wheel offset/backspacing do definitely effect the scrub radius because they change the center point of the tire contact patch relative to the scrub pivot point. Tire height affects the scrub radius as well because as the height changes, the point where the KPI angle intersects the ground changes. Neither of them affect the actual KPI angle though.