At some point you're going to have to accept that Belichickism requires Bill Belichick. Some of the FAs he's brought to the Patsies would never work anywhere else because the coaching isn't there, including Green Bay. Cheat is responsible for at least 8 Superbowl wins. Parcells was nothing without Cheat. Cheat is an exceptional coaching and GM talent, at this point I would say unquestionably the greatest in NFL history.
The Polar Bear was on a spectrum with total Draft/Development on one side and FA/Trade (George Allen) on the other. Despite your protestations, TT , though being tilted to DD side, still brought in FAs. The secret sauce for Belichickism was BB the coach being able to integrate talent and make it work in a team concept. That even included Terrell Buckley. BB the GM found a way to draw out the best last years of many a fading talent because BB the coach flawlessly deployed them.
This is my opinion: One important reason the Packers used DD so much was it was a way to indoctrinate young kids to the Green Bay life. It was a franchise survival tool to bring kids in who could live and play in a small town. So not only did they go heavy DD, but they generally selected guys mature enough to handle a city with virtually nothing to do that young kids with pockets of cash like. And veterans they brought in had to buy into that too. I'm not sure how much of a factor this is, but I'm certain it plays a part.