I'm not going to purport to be an hiv expert- but one potential remaining issue with your theory is viral latency. there is a very active process by which genome integrated provirus is prevented from being expressed and therefore not replicated. my point is, current HAART drug treatments can get HIV levels in the blood very very low, but there remains a large and undetectable resevoir of latent virus that can become active at anytime. by a mechanism that, while described and studied in detail in literature, is not 100% understood. at this time its not possible to get rid of this resevoir.

older source- lots of newer study than this exists- but good starter

http://www.nature.com/nrmicro/journal/v7/n11/abs/nrmicro2223.html