Is it possible to upgrade a holidays booking with Avios?

If so, who on Earth do I have to call (from the U.S.)? BAEC says they can't do it, and the U.S. number for BA Holidays on BA.com (1-877-428-2228) doesn't work at all (always says that "this department is currently closed"). Looking through my e-ticket receipts, the only contact mechanism listed is https://ba.com/yourquestions, but that just takes me to the main BA.com page.