I don't think you can learn your way to the cutting edge of science in a lifetime with project-based learning. In my experience it just takes too much time.
I don’t think you are at the cutting edge if you are not comfortably getting your hands dirty with it, to the point that you can clearly see what is missing and how you can further improve it.
The issue is that the "low hanging fruits" such as general relativity have been picked, the high hanging fruits require at least some kind of ladder, nuts and bolts. Perhaps a theoretician should not wire themselves the electromagnets or write the ladder logic of the PLCs running the experiments, but going up and down the stack certainly helps one's understanding and appreciation of the larger scope.
You could be hard-pressed to find a more project-based learning project than the Large Hadron Collider/James Webb Space Telescope. No amount of Gedankenexperimenten could ever prepare you for the cutting-edge science&engineering at LHC/JWST/ITER/etc.
