... I also view, terminology aside, the Eagle project to really intend to mean management of a 'large scale' (relative to the Scout's prior experience) project. ... The Positions of Responsibility are there to let the Scout find their style of leadership (as I understand you to described it)
I'm gonna pick on this statement just a bit.
REQUIREMENT 5. While a Life Scout, plan, develop, and give leadership to others in a service project helpful to any religious institution, any school, or your community. ...
This is scouting for boys -- especially this requirement, which was adopted well after BSA mandated the age limit on rank advancement.
If the Eagle project was intended to mean "management," the requirement would have said so.
If it was intended to be of a larger scale than any other projects the boy has done as a scout, it would have said so.
If positions of responsibility were intended to train in "leadership" they would all have the word "leader" on them.
I say this, because we routinely expect scouts to plan and implement service projects. The oval on their patch is immaterial. Sometimes the projects they do before Eagle are tougher than their Eagle project (albeit with fewer signatures and reporting requirements and perhaps more for the unit or a camp than for an external beneficiary). So the Eagle project is more like the debutante ball for a seasoned scout.
PoR's are simply a way to allocate management responsibilities across the members in the troop. There are jobs that need to be done, boys need to do them.
There is a synergy between the two concepts. Some leadership skill is gained while managing ... starting with leading yourself to do your appointed task. Then leading others in contributing to your task, etc ... And every time we lead (or plan, or develop) a project, we pick up some management "nugget" (e.g., task allocation, scheduling, training, after action review, etc ...). But mainly, we learn to lead (form a vision, inspire others, incorporate others, etc ...).
That's why when I look at where most leadership opportunities are throughout the advancement method, I find them in the service requirements. And, when I look at where most management opportunities are, I find them in the positions of responsibility. The really fun part, is watching it all come together when the boys work at mastering scout skills. But, IMHO, the First-Class skills are really a yard-stick to help a patrol measure its leadership and management potential.