Summary
Gephardt estimator (χ2) limited by no intrinsic dispersion and constrained by high-precision values.
FM estimator (covariance) can be artificially inflated by large error or similar sample set. Also doesn't account for error in Mbh
PCA probably the way to go, as has intrinsic dispersion and accounts for both errors. (So why didn't they use it?)
Disagreement on slope likely comes from difference in definition/estimation of σ
After renewed analysis, β really does appear to be about 4.