The fabs I've been in, have usually taken several VTs - at
least VTlin and VTsat, sometimes a scaled current density
VT (like 1uA on a 1-square device).
Doing a source-follower Vgs measurement with an appropriate
Vds, and Vbs=0, and a source current forced, is a not-useless
way to go, although it may not match any of the standard
methods especially well.
What you want out of it, would indicate how fancy a method
you want to use. Something like, say, embedding the device
in a simulation testbench so you can monitor VTN and VTP
across iterations and make sense of results / sensitivity,
probably just wants simple direct OP() from a simple bias
and call it good enough.