Quick update on my saga...

After getting many consistent confirmations from various teams, including the super-secret Spanish only group that can make manual changes, it seems apparent that Avianca will only move your flight, once, into flights in the same fare bucket. While they will not add a penalty charge, they will charge the difference in miles plus some very onerous taxes, so for all intents and purposes, they will only move you to flights where there is availability in the same fare bucket as your original award ticket. They did suggest that I get in touch with LifeMiles for a cancellation under the circumstances, but LifeMiles consistently tried to charge a $200 cancellation fee per award ticket, saying that it really isn't their issue that Avianca can't figure out how to move a flight. I was on hold for a combined 8+ hours, and also chatted with several facebook and whatsapp agents and the message was unchanged throughout.

At some point, I realized that I could move the dates by two days and that might actually work out better for me overall, and they did have availability for the new dates - so went that route, and hopefully can make it happen. They charged a phone booking fee of $30 per ticket, but I was sufficiently beaten down by that time to call it a win.