Thanks for looking up the rules for me, Tim.

However, I am still confused about which method the FAI would
actually use in a World Record claim.

The rules say that we (or they) must make a determination of
when "accurate measurement" is required:

"For accurate measurement and calculation of distance, Air Sport
Commissions shall choose which model is to be used in their area of
activity."

Assuming that a World Record requires "accurate measurement,"
the rule quoted above seems to state that the method to be used,
in the case of gliding, would be the method mandated by SC3.
The SC3 rule is:

"For the purpose of the calculation of FAI geodesic distances, the WGS84
earth model shall be used."

Given all of the above, it seems that FAI must use the ellipsoid
(and no other method) to calculate distance for the homologation
of world gliding records.

I am suspicious that they don't actually do this. Does anyone
know for sure?

And can anyone give me an example of a "non-critical" distance
measurement?