MET Rebuild Speedup, 22.0 branch (2022.09.03.)

This is a manual cherry-pick of !56373 (merged). Unfortunately that one could not be automatically cherry-picked into 22.0. (There's a difference between the configuration of AsgExampleTools between 22.0 and master. And from the looks of it, 22.0 is the more correct one...)

Please see the description in !56373 (merged) for more explanation.