I just wanted to close the loop on this with a huge thanks to two_scoops for the idea of purchasing LifeMiles. S/he was correct that Avianca insists the purchase "must be in person at an Avianca office", even though the EMD specifically reads that you may do it over the phone with the Call Center. And the closest office to me is NYC, which is a five hour drive away.

After another month and a half of calls trying to get them to adhere to their own written policy, I visited Christopher Elliott's webpage for addresses and started going up the chain with emails to higher level customer service people. Friday morning I had an additional 20,000 LifeMiles in my account which I used yesterday to offset the cost of a couple Lufthansa flights to Europe this fall.

Thank goodness that's over. Four months I'll never get back !