I have a solution! After getting totally different answers from LG's online-chat support, email support, and phone support, the phone support guy got it right. There is a bug in the version of LG Outlook Sync I downloaded from lg.com in January, and I suspect it is the same version that is still on the LG website now.
The phone support guy sent me a version that was released in 10/2009. I installed that, laboriously deleted the 100+ appointments in my phone one-by-one (there doesn't seem to be any way to clear out ALL appointments, sigh), and downloaded my appointments. Everything has the right timestamp now.
The version of LG Outlook Sync that *works* is version 10.0.0.21, dated 10/16/09. I can post it here if anybody wants it. Trust me, that would be a LOT easier than wading through LG's very confused support people.
