I am a DEM. :)
How much it might possibly move up will have a lot to do with how much of it is actually covering the cervix. I have had clients who had placentas very close and almost covering the cervix early in pregnancy. In follow-up ultrasounds the placenta had moved. However, I haven't had a client who was dxd with a complete previa.
Was it dxd as a complete previa? According to this study, a complete previa remains so.
http://www.ncbi.nlm.nih.gov/pubmed/11978274?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum
Unfortunately the majority of women who have a previa (partial or complete) will be delivered via c/s. And possibly prior to your EDD. Even when the placenta is close to the cervix and not covering it, a c/s needs to be done. As the cervix dilates, the opening becomes closer to the placenta site risking an abruption. There is an illustration here that shows what I'm talking about: http://www.moondragon.org/obgyn/pregnancy/placentaprevia.html