The “cross quadrate” is sometimes, more fully, termed a “cross nowy quadrate”. It appears to have been an artistic flourish in period, at least for discrete crosses: we’ve examples of the arms of Jerusalem with the center cross quadrate [Gelre 69v], which cannot be considered a cadency change. The treatment is accepted for Society use; difference is granted when applied to a cross throughout (i.e., an ordinary), but not when applied to a discrete cross.
Eleanor FitzPatrick bears: Per pale gules and Or, a cross quadrate couped counterchanged.