...the said movement must be performed barely off the ground and gently as a damsel might do it; it is thus the steps and movements are made in dancing the tordion.
There is a textual hint that partners stay together in the tourdion, rather than separating and performing fancy solo steps as in the galliard:
Because in dancing the tordion, one always holds the damsel by the hand and he who dances it boisterously causes needless discomfort and jolting to said damsel.
Along with the older low/high pairing of basse danse/tourdion having gone out of fashion by the time of his writing in favor of the pavane/galliard, this implication of continuous contact might account for the limited repertoire of variations. There is only so much one can comfortably vary one's steps while attached to a partner.
(The quotes above are from Mary Stewart Evans' English translation of Arbeau.)