In further researching this question, I found the following statements from the US Department of Transportation:

“refunds should be provided upon request to passengers who wish to cancel their trip as a result of a flight cancellation or significant schedule change made by the carrier” -- letter of 2001

"The second problem we wish to bring to your attention concerns passengers holding nonrefundable tickets or tickets that require the payment of a penalty for a change of flight time or travel date. It is our understanding that at least one carrier has been applying its nonrefundability/penalty provisions in situations in which the change of flight time or travel date has been necessitated by carrier action or "an act of god", e.g., where the carrier cancels a flight for weather or mechanical reasons. Imposing monetary penalties on passengers in these kinds of situations is grossly unfair and it violates 49 U.S.C. 41712, as would any contract of carriage or tariff provision mandating such a result. We will aggressively pursue any cases of this type that come to our attention." -- letter of 1996

I credit that neither of these statements specifically discusses calculation of the amount of a refund when a ticket has been partially used. Still, the language of the second quote could hardly be stronger -- "grossly unfair ... aggressively pursue". Calculating a fare difference using full-fares on flown segments, even when a passenger actually flew on a restricted fare with lower inventory and numerous other restrictions, would seem to fly in the face of these instructions from DOT.

I have contacted Cathay -- politely, of course, and with a brief request grounded in Cathay's COC rather than DOT rules. Will report back with any notable developments. Meanwhile, perhaps the above quotes can be useful to anyone facing a similar problem.